Question

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

(a) ∞

(b) 1

(c) ^1⁄2

(d) Does Not Exist

I have been asked this question in final exam.

Asked question is from Limits and Derivatives of Several Variables in division Partial Differentiation of Engineering Mathematics

Answer 1

Correct choice is (d) Does Not Exist

To elaborate: Put x = t : y = at

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

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

=a

By varying the value of a we get different limits.