Question

Given that limit exist find \(lt_{(x,y,z)\rightarrow(-9,-9,-9)}\frac{tan((x+9)(y+11)(z+7))}{(x+9)(y+10)}\)

(a) 2

(b) 1

(c) 4

(d) 3

This question was posed to me in an interview for job.

The question is from Limits and Derivatives of Several Variables in portion Partial Differentiation of Engineering Mathematics

Answer 1

Correct answer is (c) 4

The explanation is: We can parameterize the curve by

x = y = z = t

\(lt_{t\rightarrow -9}\frac{tan((t+9)(t+11)(t+7))}{(t+9)(t+10)}\)

\(lt_{t\rightarrow -9}\frac{tan((t+9)(t+11)(t+7))}{(t+9)(t+11)(t+7)}\times lt_{t\rightarrow -9}\frac{tan((t+11)(t+7))}{t+10}\)

\(=\frac{(-9+11)(-9+7)}{(-9+10)}=\frac{(2)(2)}{(1)}\)

=4