Finding Limits Section 2.1+2.2f:=x->(x^3-1)/(sqrt(x)-1);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJiokOSQiIiQiIiIhIiJGMUYxLCYtSSVzcXJ0R0YlNiNGL0YxRjJGMUYyRiVGJUYl

plot(f(x),x=-3..3,y=-5..10);

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

Digits:=20;

NiM+SSdEaWdpdHNHNiIiIz8=

for i from 1 to 10 do print(evalf(f(1+10^(-i)))) od:

NiMkIjUjPjs/VnVHZDp5JyEjPg==NiMkIjV1KTQlZSY+IkdKdmchIz4=NiMkIjUkPmNXN2A3LnYrJyEjPg==NiMkIjVzeDYuREorditnISM+NiMkIjVPJSkqXDcuK3YrKychIz4=NiMkIjUiKipcbi0rXTIrKychIz4=NiMkIjUrdlErK10yKytnISM+NiMkIjV2USsrK3YrKytnISM+NiMkIjVOKysrPzIrKytnISM+NiMkIjUrKysrZysrKytnISM+

for i from 1 to 10 do print(evalf(f(1-10^(-i)))) od;

NiMkIjVwUiMqb3JQPCQ0RyYhIz4=NiMkIjVDIz5QXXA9N2AjZiEjPg==NiMkIjVrQFh1b0NKXSMqZiEjPg==NiMkIjV4KGVvXDcuXSMqKmYhIz4=NiMkIjVnOjdESitdIyoqKmYhIz4=NiMkIjUsK2JKKytEKioqKmYhIz4=NiMkIjUrdlErK10jKioqKipmISM+NiMkIjV2USsrK0QqKioqKipmISM+NiMkIjVWKysrSyMqKioqKioqZiEjPg==NiMkIjUtKysrZysrKytnISM+

limit(f(x),x=1,right);

NiMiIic=

limit(f(x),x=1,left);

NiMiIic=

limit(f(x),x=1);

NiMiIic=

f:=x->(x^2-4)/(x-2);

NiM+SSJmRzYiZio2I0kieEdGJUYlNiRJKW9wZXJhdG9yR0YlSSZhcnJvd0dGJUYlKiYsJiokOSQiIiMiIiIhIiVGMUYxLCZGL0YxISIjRjEhIiJGJUYlRiU=

f(2);

Error, (in f) numeric exception: division by zero

plot(f,-5..5);

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

Digits:=20;

NiM+SSdEaWdpdHNHNiIiIz8=

for i from 1 to 10 do print(evalf(f(2+10^(-i)))) od:

NiMkIjUrKysrKysrKytUISM+NiMkIjUrKysrKysrKzVTISM+NiMkIjUrKysrKysrKyxTISM+NiMkIjUrKysrKysrNStTISM+NiMkIjUrKysrKysrLCtTISM+NiMkIjUrKysrKys1KytTISM+NiMkIjUrKysrKyssKytTISM+NiMkIjUrKysrKzUrKytTISM+NiMkIjUrKysrKywrKytTISM+NiMkIjUrKysrNSsrKytTISM+

for i from 1 to 10 do print(evalf(f(2-10^(-i)))) od;

NiMkIjUrKysrKysrKytSISM+NiMkIjUrKysrKysrKyEqUiEjPg==NiMkIjUrKysrKysrKyoqUiEjPg==NiMkIjUrKysrKysrISoqKlIhIz4=NiMkIjUrKysrKysrKioqKlIhIz4=NiMkIjUrKysrKyshKioqKipSISM+NiMkIjUrKysrKysqKioqKipSISM+NiMkIjUrKysrKyEqKioqKioqUiEjPg==NiMkIjUrKysrKyoqKioqKioqUiEjPg==NiMkIjUrKysrISoqKioqKioqKlIhIz4=

limit(f(x),x=2,right);limit(f(x),x=2,left);p := piecewise(x<=1,-x,x>1,x);

NiM+SSJwRzYiLUkqUElFQ0VXSVNFR0YlNiQ3JCwkSSJ4R0YlISIiMUYrIiIiNyRGKzJGLkYr

plot(p(x),x=-5..5);

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

g:=x->abs(x)/x;plot(g(x),x=-5..5);g(0);for i from 1 to 10 do print(evalf(g(0+10^(-i)))) od:for i from 1 to 10 do print(evalf(g(0-10^(-i)))) od: