Question

Find the limit.
limit x-->infinity (e^-2x)*cosx

Answer 1

\[\lim_{x\to\infty}e^{-2x}\cos x=\lim_{x\to\infty}\frac{\cos x}{e^{2x}}=\lim_{x\to\infty}\frac{1}{e^{2x}}\]
\(\cos x\) oscillates between 1 and -1 as x increases arbitrarily, so the denominator affects the actual limit.