Limit Continuity and Differentiability 1 Question 6

7. limy01+1+y42y4

(2019 Main, 9 Jan I)

(a) exists and equals 142

(b) does not exist

(c) exists and equals 122

(d) exists and equals 122(2+1)

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Answer:

Correct Answer: 7. (a)

Solution:

  1. f(x)=1x(1+|1x|)|1x|cos11x

Now, limx1f(x)=limx11x(1+1x)1xcos11x

=limx1(1x)cos11x=0

and limx1+f(x)=limx1+1x(11+x)x1cos11x

=limx1+(x+1)cos1x+1, which does not exist.



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