Question

lim x→∞ (e^(−3x)cos x)

Answer 1

\[\large\lim_{x\to\infty}e^{-3x}\cos x=\lim_{x\to\infty}\frac{\cos x}{e^{3x}}\]
Use the fact that cosine is bounded, i.e. \(-1\le\cos x\le1\).

Answer 2

last one? can you help with this one?

lim
x→(3π/2)+ (etan x)

Answer 3

Is that supposed to be \(e^{\tan x}\)?

Answer 4

yes

Answer 5

Using the continuity of the exponential function, you can rewrite:\[\large\lim_{x\to(3\pi/2)^+}e^{\tan x}=\large e^{\left(\displaystyle\lim_{x\to(3\pi/2)^+}\tan x\right)}\]