Question

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

(a) 1

(b) 0

(c) ∞

(d) Does Not Exist

I had been asked this question at a job interview.

This intriguing question originated from Limits and Derivatives of Several Variables in chapter Partial Differentiation of Engineering Mathematics

Answer 1

Correct option is (d) Does Not Exist

The explanation: Put x = t : y = at

\(=lt_{t\rightarrow 0}\frac{sin(at)}{t}\)

\(=lt_{t\rightarrow 0}a \times \frac{sin(at)}{at}=a \times lt_{t\rightarrow 0}\frac{sin(at)}{at}\)

= a * (1) = a

By varying a we get different limits

Hence, Does Not Exist is the right answer.