Question

Find \(lt_{x\rightarrow 0}\frac{sin(sin(x))}{x}\)

(a) 1

(b) ∞

(c) 0

(d) -1

The question was posed to me in a job interview.

I'm obligated to ask this question of Indeterminate Forms in chapter Differential Calculus of Engineering Mathematics

Answer 1

Correct choice is (a) 1

Easiest explanation: \(=lt_{x\rightarrow 0}(\frac{1}{x})\times(\frac{sin(x)}{1!}-\frac{(sin(x))^3}{3!}+…\infty)\)

\(=lt_{x\rightarrow 0}(\frac{sin(x)}{x.1!}-\frac{(sin(x))^3}{x.3!}+…\infty)\)

\(=lt_{x\rightarrow 0}(\frac{sin(x)}{x}-lt_{x\rightarrow 0}\frac{sin(x)}{x.3!}\times(sin(x))^2+…\infty)\)

\(=lt_{x\rightarrow 0}\frac{sin(x)}{x}=1\)