restart: #F:=(x)-> ln(x)+3/2*(x*x-1); #l:=limit( exp(x)*(cos(x))^2+(1-x/2)^2, x=0);#F:=x->exp(x)*(cos(x))^2+(1-x/2)^2; #F:=x->sin(x); #F2:=x->(1+1/x)^x; F:= t-> ln(t)+3/2*(t^2-1);

NiM+SSJGRzYiZio2I0kidEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlLCgtSSNsbkc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiM5JCIiIiokRjMiIiMjIiIkRjYjISIkRjZGNEYlRiVGJQ==

#x0:=1: t0:=1; #T4:=simplify(convert(taylor( F(x), x=x0, 8 ),'polynom')); P5:=simplify(convert(taylor( F(t), t=t0, 5 ),'polynom')); P5:=sort(%,t); #Te:=simplify(convert(taylor( F2(x), x=x0, 3 ),'polynom'));

NiM+SSN0MEc2IiIiIg==NiM+SSNQNUc2IiwsKiRJInRHRiUiIiUjISIiRikqJEYoIiIkI0YpRi0qJEYoIiIjIyEiJEYwRihGKSMhI1YiIzciIiI=NiM+SSNQNUc2IiwsKiRJInRHRiUiIiUjISIiRikqJEYoIiIkI0YpRi0qJEYoIiIjIyEiJEYwRihGKSMhI1YiIzciIiI=

#T4f:=convert(T4,'function'); f5 := t -> -1/4*t^4+4/3*t^3-3/2*t^2+4*t-43/12;

NiM+SSNmNUc2ImYqNiNJInRHRiVGJTYkSSlvcGVyYXRvckdGJUkmYXJyb3dHRiVGJSwsKiQ5JCIiJSMhIiJGLyokRi4iIiQjRi9GMyokRi4iIiMjISIkRjZGLkYvIyEjViIjNyIiIkYlRiVGJQ==

#f4 :=x-> 1/2*sin(1)+cos(1)*x-cos(1)-1/2*sin(1)*x^2+sin(1)*x; maxFehler:=evalf(F(1.5)-f5(1.5)); #maxFehler:=evalf((sin(Pi/2)-f4(Pi/2)));

NiM+SSptYXhGZWhsZXJHNiIkIihUTVUlISIq

F6:=diff(F(x), x$6 );

NiM+SSNGNkc2IiwkLUkkc2luRzYkSSpwcm90ZWN0ZWRHRipJKF9zeXNsaWJHRiU2I0kieEdGJSEiIg==

plot(abs(F6), x=-Pi/2..Pi/2);

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

X:=Pi/2: psi:=1: ObereFehlerSchranke:=-120/(psi^6*(6)!)*(X-x0)^6;

NiM+STRPYmVyZUZlaGxlclNjaHJhbmtlRzYiLCQqJCwmSSNQaUdJKnByb3RlY3RlZEdGKiMiIiIiIiMhIiJGLCIiJyNGLkYv

Tats\344chlicherFehler:=(x) -> abs(ln(x)+3/2*(x*x-1) -(5*x-227/60-7/2*x^2+10/3*x^3-5/4*x^4+1/5*x^5) );

NiM+STRUYXRzfF95Y2hsaWNoZXJGZWhsZXJHNiJmKjYjSSJ4R0YlRiU2JEkpb3BlcmF0b3JHRiVJJmFycm93R0YlRiUtSSRhYnNHSSpwcm90ZWN0ZWRHRi42IywyLUkjbG5HNiRGLkkoX3N5c2xpYkdGJTYjOSQiIiIqJkY2RjdGNkY3IyIiJCIiIyMiJFAiIiNnRjdGNiEiJiokRjZGOyMiIihGOyokRjZGOiMhIzVGOiokRjYiIiUjIiImRkcqJEY2RkkjISIiRklGJUYlRiU=

plot(Tats\344chlicherFehler(x) , x=1..1.5);

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

Tats\344chlicherFehler(Pi/2);

NiMsMC1JI2xuRzYkSSpwcm90ZWN0ZWRHRidJKF9zeXNsaWJHNiI2IywkSSNQaUdGJyMiIiIiIiMhIiIqJEYsRi8jISImIiIlIyEkUCIiI2dGLkYsIyIiJkYvKiRGLCIiJCNGOSIjNyokRixGNCNGMyIjayokRixGOSNGLiIkZyI=

evalf(%);

NiMkIihYKXpRISIq

#b)l2:=limit( ln(sin(x))/(Pi-2*x)^2, x=Pi/2);

NiM+SSNsMkc2IiMhIiIiIik=

F:=x->ln(sin(x))/(Pi-2*x)^2;

NiM+SSJGRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYtSSNsbkc2JEkqcHJvdGVjdGVkR0YwSShfc3lzbGliR0YlNiMtSSRzaW5HRi82IzkkIiIiLCZJI1BpR0YwRjdGNiEiI0Y6RiVGJUYl

x0:=1: T4:=simplify(convert(taylor( F(x), x=x0, 4 ),'polynom'));

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