Question

If f(x) = Tan(x) and g(x) = e^x – 1 than find value of limx → 0⁡ ^f(x)⁄g(x)

(a) 1

(b) 0

(c) -1

(d) 2

This question was addressed to me in examination.

My question comes from Indeterminate Forms topic in division Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (a) 1

Best explanation: \(\lim_{x\rightarrow 0}\frac{f(x)}{g(x)}=\lim_{x\rightarrow 0}\frac{tan(x)}{e^x-1}=0/0\) (Indeterminate Form)

By L’Hospital’s rule

\(\lim_{x\rightarrow 0}\frac{f(x)}{g(x)}=\lim_{x\rightarrow 0}\frac{f'(x)}{g'(x)}=\lim_{x\rightarrow 0}\frac{sec^2(x)}{e^x}\)=1