Real limits and everything else

Calculus Level pending

Which of these limits do not exist?

A) $\lim_{x\to\pi}\csc(x)e^{-x}$

B) $\lim_{x\to1}|x^3-2x^2+x-1|$

C) $\lim_{x\to\infty}\frac{e^{-x}}{\ln\left(\frac{1}{x}+1\right)}$

D) $\lim_{x\to1}\frac{x^2-1}{x-1}$

E) $\lim_{x\to0}\frac{d}{dx}(\ln(x))$

Edit: Fixed typo on E

D C and E They all exist B and C A and E A C B

1 solution

A Former Brilliant Member
Jun 15, 2020

Only in $A$ and $E$ the limits diverge. In $B$ , the limit is $1$ , in $C$ , the limit is $0$ , in $D$ , the limit is $2$ .