Evaluate the limit of the natural logarithm:

Question

the limit as x approaches infinity, e^-2xcosx

Answer 1

e^-2xcosx = cosx / e^2x

-1 ≤ cosx ≤ 1

So, -1/e^2x ≤ cosx/e^2x≤ 1/e^2x

lim_x→∞ (-1/e^2x) ≤ lim_x→∞ (cosx/e^2x) ≤ lim_x→∞ (1/e^2x)

0 ≤ lim_x→∞ (cosx/e^2x) ≤ 0

So, lim_x→∞ (cosx/e^2x) = 0