Answered: Prove that L²[−π,π] is a... |24HA

Messages Timeline Exceptions Events416 Views14 Route Queries14 Models21 Livewire0 Mails Gate Session Request

8.1.0851ms45MBGET college-homework-library/{category}/{subject}/{id}

Booting (537ms)time
Application (314ms)time
1 x Booting (63.07%)
537ms
1 x Application (36.92%)
314ms

Illuminate\Routing\Events\Routing (1.6ms)
Illuminate\Routing\Events\RouteMatched (3.13ms)
Illuminate\Foundation\Events\LocaleUpdated (6.69ms)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (247μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (216μs)
Illuminate\Database\Events\ConnectionEstablished (1.49ms)
Illuminate\Database\Events\StatementPrepared (29.41ms)
Illuminate\Database\Events\QueryExecuted (1.11ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (210μs)
eloquent.booting: App\Models\Subject (145μs)
eloquent.booted: App\Models\Subject (209μs)
Illuminate\Database\Events\StatementPrepared (2.03ms)
Illuminate\Database\Events\QueryExecuted (1.15ms)
eloquent.retrieved: App\Models\Subject (143μs)
eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (153μs)
eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (254μs)
Illuminate\Database\Events\StatementPrepared (769μs)
Illuminate\Database\Events\QueryExecuted (2.13ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (126μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (23μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (9μs)
eloquent.booting: App\Models\SubjectCat (2.05ms)
eloquent.booted: App\Models\SubjectCat (70μs)
Illuminate\Database\Events\StatementPrepared (1.47ms)
Illuminate\Database\Events\QueryExecuted (7.5ms)
eloquent.retrieved: App\Models\SubjectCat (351μs)
Illuminate\Cache\Events\CacheHit (25.44ms)
Illuminate\Cache\Events\CacheMissed (644μs)
Illuminate\Database\Events\StatementPrepared (1.25ms)
Illuminate\Database\Events\QueryExecuted (2.77ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (133μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (25μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (12μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (14μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (11μs)
Illuminate\Database\Events\StatementPrepared (1.06ms)
Illuminate\Database\Events\QueryExecuted (2.06ms)
eloquent.retrieved: App\Models\Subject (384μs)
Illuminate\Cache\Events\KeyWritten (1.92ms)
Illuminate\Database\Events\StatementPrepared (3.48ms)
Illuminate\Database\Events\QueryExecuted (9.98ms)
Illuminate\Database\Events\StatementPrepared (1.87ms)
Illuminate\Database\Events\QueryExecuted (1.26ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (52μs)
Illuminate\Database\Events\StatementPrepared (904μs)
Illuminate\Database\Events\QueryExecuted (1.02ms)
eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (42μs)
Illuminate\Cache\Events\CacheHit (792μs)
creating: homework.show (384μs)
composing: homework.show (170μs)
creating: components.breadcrumbs (395μs)
composing: components.breadcrumbs (135μs)
Illuminate\Database\Events\StatementPrepared (1.36ms)
Illuminate\Database\Events\QueryExecuted (1.02ms)
eloquent.retrieved: App\Models\SubjectCat (101μs)
Illuminate\Cache\Events\CacheMissed (16.64ms)
Illuminate\Database\Events\StatementPrepared (1.82ms)
Illuminate\Database\Events\QueryExecuted (1.37ms)
eloquent.retrieved: App\Models\SubjectCat (153μs)
Illuminate\Cache\Events\KeyWritten (725μs)
Illuminate\Cache\Events\CacheHit (485μs)
Illuminate\Cache\Events\CacheHit (431μs)
Illuminate\Cache\Events\CacheHit (432μs)
Illuminate\Cache\Events\CacheHit (310μs)
Illuminate\Cache\Events\CacheHit (393μs)
Illuminate\Cache\Events\CacheHit (248μs)
Illuminate\Cache\Events\CacheHit (231μs)
Illuminate\Cache\Events\CacheHit (265μs)
Illuminate\Cache\Events\CacheHit (374μs)
Illuminate\Cache\Events\CacheHit (466μs)
Illuminate\Cache\Events\CacheHit (328μs)
Illuminate\Cache\Events\CacheHit (577μs)
Illuminate\Cache\Events\CacheHit (4.6ms)
Illuminate\Cache\Events\CacheMissed (271μs)
Illuminate\Database\Events\StatementPrepared (700μs)
Illuminate\Database\Events\QueryExecuted (3.17ms)
eloquent.retrieved: App\Models\SubjectCat (106μs)
Illuminate\Cache\Events\KeyWritten (386μs)
Illuminate\Cache\Events\CacheHit (574μs)
Illuminate\Cache\Events\CacheHit (267μs)
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Illuminate\Cache\Events\CacheHit (175μs)
Illuminate\Cache\Events\CacheHit (305μs)
Illuminate\Cache\Events\CacheHit (213μs)
Illuminate\Cache\Events\CacheMissed (200μs)
Illuminate\Database\Events\StatementPrepared (851μs)
Illuminate\Database\Events\QueryExecuted (8.38ms)
eloquent.retrieved: App\Models\SubjectCat (106μs)
Illuminate\Cache\Events\KeyWritten (591μs)
Illuminate\Cache\Events\CacheHit (354μs)
Illuminate\Cache\Events\CacheHit (235μs)
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Illuminate\Cache\Events\CacheHit (184μs)
Illuminate\Cache\Events\CacheHit (374μs)
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Illuminate\Cache\Events\CacheHit (624μs)
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Illuminate\Cache\Events\CacheHit (252μs)
Illuminate\Cache\Events\CacheHit (6.49ms)
Illuminate\Cache\Events\CacheHit (551μs)
Illuminate\Cache\Events\CacheHit (214μs)
Illuminate\Cache\Events\CacheHit (295μs)
Illuminate\Cache\Events\CacheHit (400μs)
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Illuminate\Cache\Events\CacheHit (4.02ms)
Illuminate\Cache\Events\CacheHit (250μs)
Illuminate\Cache\Events\CacheHit (312μs)
Illuminate\Cache\Events\CacheHit (192μs)
Illuminate\Cache\Events\CacheHit (128μs)
Illuminate\Cache\Events\CacheHit (197μs)
Illuminate\Cache\Events\CacheHit (207μs)
Illuminate\Cache\Events\CacheHit (215μs)
Illuminate\Cache\Events\CacheHit (309μs)
Illuminate\Cache\Events\CacheHit (308μs)
Illuminate\Cache\Events\CacheHit (230μs)
Illuminate\Cache\Events\CacheHit (339μs)
Illuminate\Cache\Events\CacheHit (462μs)
Illuminate\Cache\Events\CacheHit (4.32ms)
Illuminate\Cache\Events\CacheHit (274μs)
Illuminate\Cache\Events\CacheHit (416μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (183μs)
Illuminate\Cache\Events\CacheHit (172μs)
Illuminate\Cache\Events\CacheHit (193μs)
Illuminate\Cache\Events\CacheHit (5.39ms)
Illuminate\Cache\Events\CacheHit (267μs)
Illuminate\Cache\Events\CacheHit (161μs)
Illuminate\Cache\Events\CacheHit (294μs)
Illuminate\Cache\Events\CacheHit (195μs)
Illuminate\Cache\Events\CacheHit (2.8ms)
Illuminate\Cache\Events\CacheHit (918μs)
Illuminate\Cache\Events\CacheHit (2.12ms)
Illuminate\Cache\Events\CacheHit (283μs)
Illuminate\Cache\Events\CacheHit (232μs)
Illuminate\Cache\Events\CacheHit (186μs)
Illuminate\Cache\Events\CacheHit (205μs)
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Illuminate\Cache\Events\CacheHit (1.12ms)
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Illuminate\Cache\Events\CacheHit (244μs)
Illuminate\Cache\Events\CacheHit (178μs)
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Illuminate\Cache\Events\CacheHit (186μs)
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creating: components.canonical (692μs)
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composing: components.open-graph (90μs)
creating: site.headers.header (288μs)
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eloquent.retrieved: App\Models\SubjectCat (83μs)
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creating: components.forms.free-tool-download (103μs)
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creating: components.forms.claim-free-worksheet (116μs)
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creating: components.forms.tutor-subscription-waitlist (103μs)
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317 x Illuminate\Cache\Events\CacheHit (19.99%)	170ms
14 x Illuminate\Database\Events\StatementPrepared (5.62%)	47.81ms
14 x Illuminate\Database\Events\QueryExecuted (5.15%)	43.84ms
5 x Illuminate\Cache\Events\CacheMissed (2.13%)	18.09ms
1 x Illuminate\Foundation\Events\LocaleUpdated (0.79%)	6.69ms
5 x Illuminate\Cache\Events\KeyWritten (0.57%)	4.88ms
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1 x eloquent.booting: App\Models\SubjectCat (0.24%)	2.05ms
1 x Illuminate\Routing\Events\Routing (0.19%)	1.60ms
1 x Illuminate\Database\Events\ConnectionEstablished (0.18%)	1.49ms
6 x eloquent.retrieved: App\Models\SubjectCat (0.11%)	900μs
1 x creating: components.canonical (0.08%)	692μs
1 x creating: site.layouts.app (0.08%)	644μs
2 x eloquent.retrieved: App\Models\Subject (0.06%)	527μs
7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)	416μs
1 x creating: components.breadcrumbs (0.05%)	395μs
1 x creating: homework.show (0.05%)	384μs
1 x creating: site.headers.header (0.03%)	288μs
1 x creating: components.forms.contact-us (0.03%)	278μs
6 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)	264μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.03%)	254μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)	247μs
1 x creating: components.open-graph (0.03%)	236μs
1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)	216μs
1 x eloquent.booted: App\Models\Subject (0.02%)	209μs
1 x composing: homework.show (0.02%)	170μs
1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)	153μs
1 x composing: components.forms.contact-us (0.02%)	153μs
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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

14 statements were executed, 5 of which were duplicates, 9 unique. Show only duplicated69.07ms

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` = '63377' limit 1

29.52mstwenty4_siteHomeworkLibraryController.php#97

Bindings	0: published 1: 0 2: 63377
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 (125)

1.08mstwenty4_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
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select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (63377)

1.63mstwenty4_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
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3.83mstwenty4_siteHomeworkLibrary.php#201

Bindings	0: 1
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select * from `solutionslibrary` where `id` <> 63377 and `subject` = 125 and `status` = 'published' and `price` > 0 order by RAND() limit 6

2.54mstwenty4_siteHomeworkLibraryRepository.php#30

Bindings	0: 63377 1: 125 2: published 3: 0
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select * from `subjects` where `subjects`.`id` in (125)

1.31mstwenty4_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

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9.95mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 63377 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` = 63377 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc

2.25mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 63377 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` = 63377 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc

1.14mstwenty4_siteHomeworkLibrary.php#260

Bindings	0: 63377 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

1.16mstwenty4_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

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

2.2mstwenty4_siteSubject.php#100

Bindings	0: 1
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1

3.14mstwenty4_siteSubject.php#100

Bindings	0: 3
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1

8.3mstwenty4_siteSubject.php#100

Bindings	0: 4
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110

select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1

1.02mstwenty4_siteSubject.php#100

Bindings	0: 36
Backtrace	18. app/Models/Subject.php:100 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419 22. app/Models/Subject.php:101 28. view::components.footer:170

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App\Models\Subject: 2Subject.php

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Prove that L²[−π,π] is a Hilbert space (i.e., show that it is separ...

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