(a) State the definition of the limit of a real-valued function as . (b) Write the…

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

(a) State the definition of the limit of a real-valued function

f(x)

x\to\infty

. (b) Write the two conditions that must be satisfied for the following statement to be true:

\displaystyle \lim_{x\to\infty}f(x)=L

. (c) Let

g(x)=e^{-x}\cos x

. Using only the facts that

|\cos x|\le 1

for all real

x

and that

\displaystyle \lim_{x\to\infty}e^{-x}=0

, explain in words why

\displaystyle \lim_{x\to\infty}g(x)=0