NIMCET 2026 Mathematics Question 22 with Solution

Question 22

Mathematics Limit of Functions Hard

Which of the following is NOT true?

(A) \(\lim _{{x}\rightarrow\infty}\frac{x}{{e}^x}=0\)

(B) \(\lim _{{x}\rightarrow0+}\frac{1}{{xe}^{1/x}}=0\)

(C) \(\lim _{{x}\rightarrow0+}\frac{\sin x}{{1+2x}}=0\)

(D) \(\lim _{{x}\rightarrow0+}\frac{\cos x}{{1+2x}}=0\)

View Dynamic Solution & Explanation ▼

Correct Solution: Option D

Step-by-step Solution:

The fourth choice is not correct, as the limit \[ \lim_{x \to 0^+} \frac{\cos x}{1 + 2x} = 0. \]