Loading [MathJax]/jax/output/HTML-CSS/jax.js


1)

Let 

   f(x)=1x(1+1x)1xcos(11x)   for x≠ 1, then


A) limx1+f(x)=0

B) limx1+f(x) doesnot exist

C) limx1f(x)=0

D) limx1f(x) doesnot exist

Answer:

Option B,C

Explanation:

f(x)=1x(1+1x)1xcos(11x)

Now, 

     limx1f(x)

=limx11x(1+1x)1xcos(11x)

=limx1(1x)cos(11x)=0andlimx1+f(x)=limx1+

1x(11+x)x1cos(11x)

=limx1+(x+1)cos(1x+1) where x≠ 1 doesnot exist