MapleLimitEx.mws

Limit Examples

Use these examples for Maple syntax.

Using "Limit" with a capital "L" produces a statement which can be evaluated with "value(%)".  The "%" relates to the last executed statement.  Using "limit" with a small "l" computes the limit immediately.

>    Limit((x^2-9)/(x-3),x=3);

Limit((x^2-9)/(x-3),x = 3)

>    value(%);

6

>    limit((x^2-9)/(x-3),x=3);

6

>    Limit(sin(x)/x,x=0);

Limit(sin(x)/x,x = 0)

>    value(%);

1

>    limit(sin(x)/x,x=0);

1

>    Limit((sqrt(2+x)-sqrt(2))/x,x=0);

Limit(((2+x)^(1/2)-2^(1/2))/x,x = 0)

>    value(%);

1/4*2^(1/2)

>    limit((sqrt(x+1)-2)/(x-3),x=3);

1/4

>    Limit((1/(x+4)-1/4)/x,x=0);

Limit((1/(x+4)-1/4)/x,x = 0)

>    value(%);

-1/16

>    limit(sin(7*x)/(3*x),x=0);

7/3

Limits at infinity and left and right hand limits can be computed.

>    Limit((3*x^3-4*x+8)/(2*x^3+100*x^2),x=infinity);

Limit((3*x^3-4*x+8)/(2*x^3+100*x^2),x = infinity)

>    value(%);

3/2

>    limit((3*x^3-4*x+8)/(2*x^3+100*x^2),x=infinity);

3/2

>    Limit((3*x^2-4*x+8)/(2*x^3+100*x^2),x=infinity);

Limit((3*x^2-4*x+8)/(2*x^3+100*x^2),x = infinity)

>    limit((3*x^2-4*x+8)/(2*x^3+100*x^2),x=infinity);

0

>    Limit((3*x^4-4*x+8)/(2*x^3+100*x^2),x=infinity);

Limit((3*x^4-4*x+8)/(2*x^3+100*x^2),x = infinity)

>    limit((3*x^4-4*x+8)/(2*x^3+100*x^2),x=infinity);

infinity

>    Limit(x^2/(x+4),x=-4);

Limit(x^2/(x+4),x = -4)

>    value(%);

undefined

>    Limit(x^2/(x+4),x=-4,left);

Limit(x^2/(x+4),x = -4,left)

>    value(%);

-infinity

>    Limit(x^2/(x+4),x=-4,right);

Limit(x^2/(x+4),x = -4,right)

>    value(%);

infinity

>