Some Limits with Maple

> f:=(-x^2+3*x-2)/(x^4+5*x^3+x^2-21*x-18);

f := (-x^2+3*x-2)/(x^4+5*x^3+x^2-21*x-18)

> limit(f,x=2);

-1/75

> limit(f,x=1);

0

> limit(f,x=0);

1/9

> limit(f,x=-3);

-infinity

> limit(f,x=-1);

undefined

> f:=(sqrt(4-h)-sqrt(4))/h;

f := (sqrt(4-h)-2)/h

> limit(f,h=0);

-1/4

> f:=(sqrt(a-h)-sqrt(a))/h;

f := (sqrt(a-h)-sqrt(a))/h

> limit(f,h=0);

-1/2*1/(sqrt(a))

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