Which of the following statements is TRUE about ( _ x a f(x) g(x) ) when (f

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following statements is TRUE about

\displaystyle \lim_{x\to a}\frac{f(x)}{g(x)}

when

f(a)=g(a)=0

? (a) The limit equals

0

because both numerator and denominator become zero at

x=a

. (b) The limit can be obtained by differentiating numerator and denominator once and then substituting

x=a

. (c) If both

f(x)

and

g(x)

contain a common non-zero factor

(x-a)

, cancelling that factor may make the limit computable. (d) The limit exists only when the degree of

f(x)

is less than the degree of

g(x)