Limit Terms / Definitions

If lim (x->a-) f(x)=L and lim (x->a+) f(x) = M, where L and M are infinite real numbers, then what must be true about L and M in order for lim (x->a) f(x) to exist?

L=M

What is a vertical asymptote?

A vertical asymptote is a vertical line x = a, which the group of a function approaches as x approaches a

T of F. When lim (x->a) f(x) exists, it always equals f(a). State whether this statement is true or false

False. The limit (if it exists) depends on values of f near a, but it does not depend on the value of f(a)

Explain the meaning of lim(x->a-) r(X) = L

As x approaches a from the left, the value of r(x) approaches L

Explain why lim (x->-2) (x^2+8x+12)/(x+2) = lim (x->-2) (x+6), and then evaluate lim (x->-2) (x^2+8x+12)/(x+2)

Since (x^2+8x+12)/(x+2) = x+6 whenever x/=/-2, it follows that the two expressions evaluate to the same number as x approaches -2

For what values of a does lim (x->a) r(x) = r(a) if r is a rational function?

The values of a for which the denominator of the function r is not zero

How is lim (x->a) p(x) calculated if p is a polynomial function

lim (x->a) p(x) = p(a)