Consider f(x)=(x-1)/(x+1) for all x≠-1. (a) Find Taylor series f...

Question
Consider f(x)=(x-1)/(x+1) for all x≠-1.

(a) Find Taylor series for f(x) about x=1 of powers in ascending order, showing terms up to (x-1)⁴.

(b) Write the nth term of the power series obtained in part (a).

(c) Determine all values of x such that f(x) equals to its Taylor series about x=1
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      • Illuminate\Cache\Events\CacheHit (189μs)
      • Illuminate\Cache\Events\CacheHit (169μs)
      • Illuminate\Cache\Events\CacheHit (181μs)
      • Illuminate\Cache\Events\CacheHit (157μs)
      • creating: site.layouts.app (660μs)
      • composing: site.layouts.app (21μs)
      • creating: components.canonical (459μs)
      • composing: components.canonical (150μs)
      • creating: components.open-graph (337μs)
      • composing: components.open-graph (86μs)
      • creating: site.headers.header (333μs)
      • composing: site.headers.header (80μs)
      • Illuminate\Cache\Events\CacheHit (2ms)
      • creating: components.footer (81μs)
      • composing: components.footer (92μs)
      • Illuminate\Cache\Events\CacheHit (1.01ms)
      • Illuminate\Cache\Events\CacheMissed (464μs)
      • Illuminate\Database\Events\StatementPrepared (915μs)
      • Illuminate\Database\Events\QueryExecuted (1.12ms)
      • eloquent.retrieved: App\Models\SubjectCat (58μs)
      • Illuminate\Cache\Events\KeyWritten (441μs)
      • Illuminate\Cache\Events\CacheHit (330μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (137μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (280μs)
      • Illuminate\Cache\Events\CacheHit (347μs)
      • Illuminate\Cache\Events\CacheHit (188μs)
      • Illuminate\Cache\Events\CacheHit (196μs)
      • Illuminate\Cache\Events\CacheHit (183μs)
      • Illuminate\Cache\Events\CacheHit (211μs)
      • Illuminate\Cache\Events\CacheHit (293μs)
      • creating: components.forms.contact-us (311μs)
      • composing: components.forms.contact-us (200μs)
      • creating: components.forms.get-started (215μs)
      • composing: components.forms.get-started (91μs)
      • creating: components.forms.free-tool-download (152μs)
      • composing: components.forms.free-tool-download (142μs)
      • creating: components.forms.claim-free-worksheet (155μs)
      • composing: components.forms.claim-free-worksheet (80μs)
      • creating: components.forms.tutor-subscription-waitlist (284μs)
      • composing: components.forms.tutor-subscription-waitlist (275μs)
      • creating: components.forms.tutor-subscription-join (159μs)
      • composing: components.forms.tutor-subscription-join (152μs)
      • creating: components.forms.tutor-support (247μs)
      • composing: components.forms.tutor-support (64μs)
      • 312 x Illuminate\Cache\Events\CacheHit (18.53%)
        130ms
        19 x Illuminate\Database\Events\QueryExecuted (7.77%)
        54.41ms
        19 x Illuminate\Database\Events\StatementPrepared (6.37%)
        44.62ms
        10 x Illuminate\Cache\Events\KeyWritten (1.96%)
        13.70ms
        10 x Illuminate\Cache\Events\CacheMissed (1.55%)
        10.88ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.24%)
        8.71ms
        11 x eloquent.retrieved: App\Models\SubjectCat (0.32%)
        2.22ms
        1 x Illuminate\Routing\Events\Routing (0.25%)
        1.73ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.24%)
        1.66ms
        5 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.12%)
        815μs
        1 x creating: homework.show (0.11%)
        803μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.11%)
        742μs
        1 x creating: site.layouts.app (0.09%)
        660μs
        1 x Illuminate\Routing\Events\RouteMatched (0.08%)
        557μs
        1 x creating: components.breadcrumbs (0.08%)
        540μs
        1 x creating: components.canonical (0.07%)
        459μs
        1 x eloquent.booting: App\Models\SubjectCat (0.06%)
        436μs
        1 x creating: components.open-graph (0.05%)
        337μs
        1 x creating: site.headers.header (0.05%)
        333μs
        1 x creating: components.forms.contact-us (0.04%)
        311μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.04%)
        309μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.04%)
        284μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.04%)
        275μs
        2 x eloquent.retrieved: App\Models\Subject (0.04%)
        258μs
        1 x composing: components.breadcrumbs (0.04%)
        258μs
        1 x creating: components.forms.tutor-support (0.04%)
        247μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.03%)
        236μs
        1 x creating: components.forms.get-started (0.03%)
        215μs
        1 x composing: components.forms.contact-us (0.03%)
        200μs
        1 x creating: components.forms.tutor-subscription-join (0.02%)
        159μs
        1 x creating: components.forms.claim-free-worksheet (0.02%)
        155μs
        1 x creating: components.forms.free-tool-download (0.02%)
        152μs
        1 x composing: components.forms.tutor-subscription-join (0.02%)
        152μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        151μs
        1 x composing: components.canonical (0.02%)
        150μs
        1 x composing: components.forms.free-tool-download (0.02%)
        142μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        138μs
        1 x composing: homework.show (0.02%)
        136μs
        1 x eloquent.booted: App\Models\SubjectCat (0.02%)
        115μs
        1 x composing: components.footer (0.01%)
        92μs
        1 x composing: components.forms.get-started (0.01%)
        91μs
        1 x composing: components.open-graph (0.01%)
        86μs
        1 x creating: components.footer (0.01%)
        81μs
        1 x composing: site.headers.header (0.01%)
        80μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        80μs
        1 x composing: components.forms.tutor-support (0.01%)
        64μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        63μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        62μs
        1 x composing: site.layouts.app (0%)
        21μs
      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
      19 statements were executed, 5 of which were duplicates, 14 unique. Show only duplicated68.92ms
      • 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` = '20657' limit 1
        14.85mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 20657
        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 (6)
        1.86mstwenty4_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 (20657)
        4.01mstwenty4_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
        1.17mstwenty4_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` <> 20657 and `subject` = 6 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        20.49mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 20657
        • 1: 6
        • 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 (6)
        1.21mstwenty4_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` = 20657 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        7.19mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20657
        • 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` = 20657 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        2.1mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20657
        • 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` = 20657 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        1.82mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 20657
        • 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
        1.37mstwenty4_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
        1.21mstwenty4_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
        1.39mstwenty4_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` = 10 limit 1
        2.05mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        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` = 33 limit 1
        1.32mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        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` = 11 limit 1
        1.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        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` = 5 limit 1
        1.7mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        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` = 34 limit 1
        1.2mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        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` = 31 limit 1
        1.48mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        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
        1.23mstwenty4_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
      App\Models\SubjectCat
      11SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      5HomeworkLibraryFile.php
      App\Models\Subject
      2Subject.php
          _token
          AqwbYirPhCuc9oJ3ZeXfGWV9VWTmbA1MOL4mPBaX
          utm_source
          direct
          redirectUrl
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          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Mathematics/Cal...
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          PHPDEBUGBAR_STACK_DATA
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          path_info
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          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
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          request_query
          []
          
          request_request
          []
          
          request_headers
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          request_cookies
          []
          
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