Limit Continuity and Differentiability 1 Question 13

14. The integer n for which limx0(cosx1)(cosxex)xn is a finite non-zero number, is

(2002, 2M)

(a) 1

(b) 2

(c) 3

(d) 4

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Answer:

Correct Answer: 14. (c)

Solution:

  1. limx01+5x21+3x21/x2=limx0[(1+5x2)1/5x2]5limx0[(1+3x2)1/3x2]3=e5e3=e2

=elimx5(x+4)x+1=e5



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