Answered: Find the lim nx(1-x)ᶯ as n tends to inf... |24HA

Messages Timeline Exceptions Events402 Views14 Route Queries10 Models19 Livewire0 Mails Gate Session Request

8.1.0869ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (548ms)time
Application (322ms)time
1 x Booting (63.01%)
548ms
1 x Application (36.99%)
322ms

Illuminate\Routing\Events\Routing (1.02ms)
Illuminate\Routing\Events\RouteMatched (353μs)
Illuminate\Foundation\Events\LocaleUpdated (4.02ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (199μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (159μs)
Illuminate\Database\Events\ConnectionEstablished (775μs)
Illuminate\Database\Events\StatementPrepared (11.65ms)
Illuminate\Database\Events\QueryExecuted (1.53ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (121μs)
eloquent.booting: App\Models\Subject (76μs)
eloquent.booted: App\Models\Subject (57μs)
Illuminate\Database\Events\StatementPrepared (2.6ms)
Illuminate\Database\Events\QueryExecuted (1.88ms)
eloquent.retrieved: App\Models\Subject (130μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (123μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (57μs)
Illuminate\Database\Events\StatementPrepared (2.28ms)
Illuminate\Database\Events\QueryExecuted (3.59ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (461μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (35μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (14μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (10μs)
eloquent.booting: App\Models\SubjectCat (3.52ms)
eloquent.booted: App\Models\SubjectCat (90μs)
Illuminate\Database\Events\StatementPrepared (1.11ms)
Illuminate\Database\Events\QueryExecuted (1.12ms)
eloquent.retrieved: App\Models\SubjectCat (127μs)
Illuminate\Cache\Events\CacheHit (33.6ms)
Illuminate\Cache\Events\CacheMissed (268μs)
Illuminate\Database\Events\StatementPrepared (1.05ms)
Illuminate\Database\Events\QueryExecuted (35.72ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (162μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (110μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (47μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (116μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (44μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (16μs)
Illuminate\Database\Events\StatementPrepared (1.05ms)
Illuminate\Database\Events\QueryExecuted (1.26ms)
eloquent.retrieved: App\Models\Subject (160μs)
Illuminate\Cache\Events\KeyWritten (1.18ms)
Illuminate\Database\Events\StatementPrepared (1.64ms)
Illuminate\Database\Events\QueryExecuted (1.38ms)
Illuminate\Database\Events\StatementPrepared (858μs)
Illuminate\Database\Events\QueryExecuted (1.46ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (60μs)
Illuminate\Database\Events\StatementPrepared (809μs)
Illuminate\Database\Events\QueryExecuted (1.21ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (48μs)
Illuminate\Cache\Events\CacheHit (475μs)
creating: homework.show (282μs)
composing: homework.show (106μs)
creating: components.breadcrumbs (272μs)
composing: components.breadcrumbs (120μs)
Illuminate\Database\Events\StatementPrepared (1.32ms)
Illuminate\Database\Events\QueryExecuted (1.55ms)
eloquent.retrieved: App\Models\SubjectCat (87μs)
Illuminate\Cache\Events\CacheHit (5.8ms)
Illuminate\Cache\Events\CacheHit (211μs)
Illuminate\Cache\Events\CacheHit (221μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (209μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (362μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (201μs)
Illuminate\Cache\Events\CacheHit (217μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (205μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (198μs)
Illuminate\Cache\Events\CacheHit (173μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (182μs)
Illuminate\Cache\Events\CacheHit (168μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (271μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (152μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (149μs)
Illuminate\Cache\Events\CacheHit (2.05ms)
Illuminate\Cache\Events\CacheHit (433μs)
Illuminate\Cache\Events\CacheHit (1.9ms)
Illuminate\Cache\Events\CacheHit (472μs)
Illuminate\Cache\Events\CacheHit (3.61ms)
Illuminate\Cache\Events\CacheHit (236μs)
Illuminate\Cache\Events\CacheHit (10.42ms)
Illuminate\Cache\Events\CacheHit (315μs)
Illuminate\Cache\Events\CacheHit (332μs)
Illuminate\Cache\Events\CacheHit (1.67ms)
Illuminate\Cache\Events\CacheHit (299μs)
Illuminate\Cache\Events\CacheHit (235μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (326μs)
Illuminate\Cache\Events\CacheHit (179μs)
Illuminate\Cache\Events\CacheHit (599μs)
Illuminate\Cache\Events\CacheHit (247μs)
Illuminate\Cache\Events\CacheHit (169μs)
Illuminate\Cache\Events\CacheHit (704μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (290μs)
Illuminate\Cache\Events\CacheHit (1.12ms)
Illuminate\Cache\Events\CacheHit (554μs)
Illuminate\Cache\Events\CacheHit (13.9ms)
Illuminate\Cache\Events\CacheHit (433μs)
Illuminate\Cache\Events\CacheHit (259μs)
Illuminate\Cache\Events\CacheHit (1.04ms)
Illuminate\Cache\Events\CacheHit (419μs)
Illuminate\Cache\Events\CacheHit (228μs)
Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (257μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (227μs)
Illuminate\Cache\Events\CacheHit (210μs)
Illuminate\Cache\Events\CacheHit (222μs)
Illuminate\Cache\Events\CacheHit (281μs)
Illuminate\Cache\Events\CacheHit (517μs)
Illuminate\Cache\Events\CacheHit (202μs)
Illuminate\Cache\Events\CacheHit (270μs)
Illuminate\Cache\Events\CacheHit (362μs)
Illuminate\Cache\Events\CacheHit (273μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (189μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (180μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (215μs)
Illuminate\Cache\Events\CacheHit (199μs)
Illuminate\Cache\Events\CacheHit (176μs)
Illuminate\Cache\Events\CacheHit (277μs)
Illuminate\Cache\Events\CacheHit (185μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (298μs)
Illuminate\Cache\Events\CacheHit (268μs)
Illuminate\Cache\Events\CacheHit (305μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (166μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (162μs)
Illuminate\Cache\Events\CacheHit (196μs)
Illuminate\Cache\Events\CacheHit (170μs)
Illuminate\Cache\Events\CacheHit (330μs)
Illuminate\Cache\Events\CacheHit (164μs)
Illuminate\Cache\Events\CacheHit (190μs)
Illuminate\Cache\Events\CacheHit (165μs)
Illuminate\Cache\Events\CacheHit (1.62ms)
Illuminate\Cache\Events\CacheHit (394μs)
Illuminate\Cache\Events\CacheHit (315μs)
Illuminate\Cache\Events\CacheHit (290μs)
Illuminate\Cache\Events\CacheHit (1.07ms)
Illuminate\Cache\Events\CacheHit (200μs)
Illuminate\Cache\Events\CacheHit (436μs)
Illuminate\Cache\Events\CacheHit (194μs)
Illuminate\Cache\Events\CacheHit (390μs)
Illuminate\Cache\Events\CacheHit (269μs)
Illuminate\Cache\Events\CacheHit (547μs)
Illuminate\Cache\Events\CacheHit (419μs)
Illuminate\Cache\Events\CacheHit (502μs)
Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (216μs)
Illuminate\Cache\Events\CacheHit (188μs)
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Illuminate\Cache\Events\CacheHit (184μs)
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Illuminate\Cache\Events\CacheHit (350μs)
Illuminate\Cache\Events\CacheHit (267μs)
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Illuminate\Cache\Events\CacheHit (320μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (199μs)
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Illuminate\Cache\Events\CacheHit (181μs)
Illuminate\Cache\Events\CacheHit (161μs)
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Illuminate\Cache\Events\CacheHit (177μs)
Illuminate\Cache\Events\CacheHit (158μs)
Illuminate\Cache\Events\CacheHit (14.42ms)
Illuminate\Cache\Events\CacheHit (514μs)
Illuminate\Cache\Events\CacheHit (390μs)
Illuminate\Cache\Events\CacheHit (188μs)
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Illuminate\Cache\Events\CacheHit (168μs)
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Illuminate\Cache\Events\CacheHit (150μs)
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Illuminate\Cache\Events\CacheHit (324μs)
Illuminate\Cache\Events\CacheHit (228μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (226μs)
Illuminate\Cache\Events\CacheHit (271μs)
Illuminate\Cache\Events\CacheHit (220μs)
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Illuminate\Cache\Events\CacheHit (496μs)
Illuminate\Cache\Events\CacheHit (531μs)
Illuminate\Cache\Events\CacheHit (543μs)
creating: site.layouts.app (480μs)
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creating: components.canonical (606μs)
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creating: site.headers.header (412μs)
composing: site.headers.header (165μs)
Illuminate\Cache\Events\CacheHit (1.74ms)
creating: components.footer (83μs)
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Illuminate\Cache\Events\CacheHit (993μs)
Illuminate\Cache\Events\CacheHit (441μs)
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creating: components.forms.contact-us (273μs)
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creating: components.forms.get-started (692μs)
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creating: components.forms.free-tool-download (333μs)
composing: components.forms.free-tool-download (87μs)
creating: components.forms.claim-free-worksheet (189μs)
composing: components.forms.claim-free-worksheet (79μs)
creating: components.forms.tutor-subscription-waitlist (109μs)
composing: components.forms.tutor-subscription-waitlist (69μs)
creating: components.forms.tutor-subscription-join (98μs)
composing: components.forms.tutor-subscription-join (155μs)
creating: components.forms.tutor-support (143μs)
composing: components.forms.tutor-support (76μs)

321 x Illuminate\Cache\Events\CacheHit (25.32%)	220ms
10 x Illuminate\Database\Events\QueryExecuted (5.83%)	50.71ms
10 x Illuminate\Database\Events\StatementPrepared (2.8%)	24.37ms
1 x Illuminate\Foundation\Events\LocaleUpdated (0.46%)	4.02ms
1 x eloquent.booting: App\Models\SubjectCat (0.4%)	3.52ms
1 x Illuminate\Cache\Events\KeyWritten (0.14%)	1.18ms
1 x Illuminate\Routing\Events\Routing (0.12%)	1.02ms
1 x Illuminate\Database\Events\ConnectionEstablished (0.09%)	775μs
1 x creating: components.forms.get-started (0.08%)	692μs
8 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.07%)	649μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)	616μs
1 x creating: components.canonical (0.07%)	606μs
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1 x creating: components.open-graph (0.05%)	408μs
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1 x composing: components.forms.get-started (0.04%)	349μs
1 x creating: components.forms.free-tool-download (0.04%)	333μs
2 x eloquent.retrieved: App\Models\Subject (0.03%)	290μs
1 x creating: homework.show (0.03%)	282μs
1 x composing: components.forms.contact-us (0.03%)	278μs
1 x creating: components.forms.contact-us (0.03%)	273μs
1 x creating: components.breadcrumbs (0.03%)	272μs
1 x Illuminate\Cache\Events\CacheMissed (0.03%)	268μs
2 x eloquent.retrieved: App\Models\SubjectCat (0.02%)	214μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)	199μs
1 x creating: components.forms.claim-free-worksheet (0.02%)	189μs
1 x composing: site.headers.header (0.02%)	165μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.02%)	159μs
1 x composing: components.forms.tutor-subscription-join (0.02%)	155μs
1 x creating: components.forms.tutor-support (0.02%)	143μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)	123μs
1 x composing: components.breadcrumbs (0.01%)	120μs
1 x creating: components.forms.tutor-subscription-waitlist (0.01%)	109μs
1 x composing: components.canonical (0.01%)	108μs
1 x composing: homework.show (0.01%)	106μs
1 x composing: components.open-graph (0.01%)	102μs
1 x creating: components.forms.tutor-subscription-join (0.01%)	98μs
1 x composing: components.footer (0.01%)	93μs
1 x eloquent.booted: App\Models\SubjectCat (0.01%)	90μs
1 x composing: components.forms.free-tool-download (0.01%)	87μs
1 x creating: components.footer (0.01%)	83μs
1 x composing: components.forms.claim-free-worksheet (0.01%)	79μs
1 x eloquent.booting: App\Models\Subject (0.01%)	76μs
1 x composing: components.forms.tutor-support (0.01%)	76μs
1 x composing: components.forms.tutor-subscription-waitlist (0.01%)	69μs
1 x eloquent.booted: App\Models\Subject (0.01%)	57μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)	57μs
1 x composing: site.layouts.app (0%)	25μs

14 templates were rendered

1x homework.showshow.blade.phpblade
1x components.breadcrumbsbreadcrumbs.blade.phpblade
1x site.layouts.appapp.blade.phpblade
1x components.canonicalcanonical.blade.phpblade
1x components.open-graphopen-graph.blade.phpblade
1x site.headers.headerheader.blade.phpblade
1x components.footerfooter.blade.phpblade
1x components.forms.contact-uscontact-us.blade.phpblade
1x components.forms.get-startedget-started.blade.phpblade
1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
1x components.forms.tutor-supporttutor-support.blade.phpblade

uri: GET college-homework-library/{category}/{subject}/{id}
middleware: web, utm.parameters
controller: App\Http\Controllers\HomeworkLibraryController@show
namespace
where
as: homework.show
file: app/Http/Controllers/HomeworkLibraryController.php:79-176

10 statements were executed, 4 of which were duplicates, 6 unique. Show only duplicated63.02ms

Connection Establishedtwenty4_siteHomeworkLibraryController.php#91

Backtrace

13. app/Http/Controllers/HomeworkLibraryController.php:91
14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '61066' limit 1

12.21mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 61066
Backtrace	16. app/Http/Controllers/HomeworkLibraryController.php:97 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `subjects` where `subjects`.`id` in (60)

2.82mstwenty4_siteHomeworkLibraryController.php#97

Backtrace

21. app/Http/Controllers/HomeworkLibraryController.php:97
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (61066)

4.94mstwenty4_siteHomeworkLibraryController.php#97

Backtrace

21. app/Http/Controllers/HomeworkLibraryController.php:97
22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205

select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1

1.25mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 1
Backtrace	20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201 26. app/Http/Controllers/HomeworkLibraryController.php:105 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260

select * from `solutionslibrary` where `id` <> 61066 and `subject` = 60 and `status` = 'published' and `price` > 0 order by RAND() limit 6

35.13mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 61066 1: 60 2: published 3: 0
Backtrace	14. app/Repositories/HomeworkLibraryRepository.php:30 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 18. app/Repositories/HomeworkLibraryRepository.php:39 19. app/Http/Controllers/HomeworkLibraryController.php:139

select * from `subjects` where `subjects`.`id` in (60)

1.22mstwenty4_siteHomeworkLibraryRepository.php#30

Backtrace

19. app/Repositories/HomeworkLibraryRepository.php:30
20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
23. app/Repositories/HomeworkLibraryRepository.php:39
24. app/Http/Controllers/HomeworkLibraryController.php:139

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61066 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc

1.3mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 61066 1: question
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61066 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

1.26mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 61066 1: teaser
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 61066 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

1.2mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 61066 1: solution
Backtrace	15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80 19. vendor/league/fractal/src/TransformerAbstract.php:128 20. vendor/league/fractal/src/TransformerAbstract.php:107 21. vendor/league/fractal/src/Scope.php:383

select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1

1.69mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 1
Backtrace	20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70

App\Models\HomeworkLibrary\HomeworkLibraryFile: 8HomeworkLibraryFile.php
App\Models\HomeworkLibrary\HomeworkLibrary: 7HomeworkLibrary.php
App\Models\Subject: 2Subject.php
App\Models\SubjectCat: 2SubjectCat.php

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Find the lim nx(1-x)ᶯ as n tends to infinity. x belongs to [0,1]

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