Question

\(\lim_{x\rightarrow 0}⁡\frac{x^2 Sin(x) – e^{x^2}}{Cos⁡(x+π/2)}\) is

(a) 0

(b) 1

(c) 2

(d) 3

The question was asked at a job interview.

This intriguing question comes from Indeterminate Forms topic in portion Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (a) 0

The explanation: \(\lim_{x\rightarrow 0}⁡\frac{x^2 Sin(x) – e^{x^2}}{Cos⁡(x+π/2)}\)=-1/0 (Indeterminate form)

By L’Hospital rule

\(\lim_{x\rightarrow 0}⁡\frac{x^2 Sin(x) – e^{x^2}}{Cos⁡(x+π/2)}\)

\(=\lim_{x\rightarrow 0}⁡\frac{x^2 Cos(x) + 2xSin(x) – 2xe^{x^2}}{-Sin(x+π/2)}\)= 0