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function Question2()

%clamped spline has endtype 2

%f(x)=x e^(-6x)   f'(x)=(1-6x)e^(-6x)
%f''(x)=(-12+36x)e^(-6x)

f=@(x)(x.* exp(-6*x));   df=@(x)((1-6*x).*exp(-6*x));
endtype=2;
h=zeros(1,5);
enum=zeros(1,5);%vector of errors
alpha=zeros(1,5);%vector of orders of precision
X=0:0.001:1;
for k=1:5
n=2^k;
h(k)=1/n;
x=0:h(k):1;
Y2=[df(0),f(x),df(1)];
[pp2]=myspline(x,Y2,endtype);
[breaks2, coefs2]=unmkpp(pp2);
enum(k)=max(abs(ppval(pp2,X)-f(X)));
end

for k=2:5
    alpha(k)=log(enum(k)/enum(k-1))/log(h(k)/h(k-1));
end
EnumClampedSpline=enum
alphaClampedSpline=alpha
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      • creating: site.layouts.app (621μs)
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        • 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
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        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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        970μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
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        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
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        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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        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
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        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
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        • 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
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        1.44mstwenty4_siteSubject.php#100
        Bindings
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        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
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        Bindings
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        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
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