Problem:
Investigate the evaluation of limits with a computer algebra system.
Visualization:
Using Maple:

The Maple command for

is limit(f(x), x=a).

The following are some examples of the use of this command including some which are used in other Visual Calculus modules on limits.

> limit((x^2-5*x+4)/(x-1),x=1);

- 3

> limit(sin(x)/x,x=0);

1

> limit(sin(n*x)/x,x=0);

n

> limit(((x^3+8)^(1/3)-2)/x^3,x=0);

> limit(sin(10*Pi/x),x=0);

- 1 .. 1

> limit(x*sin(1/x),x=0);

0

> limit((x^2+1)/(x-1),x=1);

undefined

> g:=x->abs(x)/x;

> limit(g(x),x=0);

undefined

> limit(g(x),x=0,right);

1

> limit(g(x),x=0,left);

- 1

> limit((1+x)^(1/x),x=0);

e

> limit((8^x-5^x)/x,x=0);

3 ln(2) - ln(5)

> k:=x->(3*x-15)/(x^2-10*x+25)^(1/2);

> limit(k(x),x=5);

undefined

> limit(k(x),x=5,right);

3

> limit(k(x),x=5,left);

- 3