Question

Value of limx → 0[(1+xe^x)/(1 – Cos(x))].

(a) e

(b) 1

(c) 2

(d) Can not be solved

I had been asked this question in final exam.

Question is from Limits and Derivatives of Several Variables in chapter Partial Differentiation of Engineering Mathematics

Answer 1

The correct option is (c) 2

Easy explanation: =>limx → 0[(1+xe^x)/(1 – Cos(x))] = ^1⁄0 (Indeterminate)

=> By L’Hospital rule

=> limx → 0[(1+xe^x) / (Sin(x))] = ^1⁄0 (Again indeterminate)

=> By L’ Hospital rule

=> limx → 0[((2+x)e^x)/ (Cos(x))] = 2.