Question

lim (e^2002x+1)-(1-1001x)(e^1001x-e^-1001x)/x(e^x-1)

Answer 1

Prove this by the LHL RHL method

Explanation:

• Given $\lim_{x \to 0} \frac{e^\frac{1}{x} -1}{e^\frac{1}{x} +1}$

• remember $e^\infty = \infty\\\\e^-^\infty = 0$

• put $x=0-$ to get LHL as $-1$

• put $x=0+$ to get RHL as $+1$

• $as LHL \ne RHL$, Limit does not exist.