Mathematics

Problem

Evaluate the following limits and give a brief justification for each answer. Show all necessary steps. a. (a)

\displaystyle \lim_{x\to 0}\bigl(2e^{x}+\sin x\bigr)

b. (b)

\displaystyle \lim_{x\to \pi/6}\bigl(\sqrt{3}\,\cos x-2\sin x\bigr)

c. (c) For

g(x)=\ln(5x-1)

, compute

\displaystyle \lim_{x\to 1} g(x)

and interpret the result in terms of the behaviour of

g

near

x=1