1. find the limit lim x to zero (sin^2 2x)/x^2 a)0 b)1 c) 2 d)4 3)none of the ab

Question

1. find the limit  

   lim x to zero  (sin^2 2x)/x^2

a)0   b)1  c) 2  d)4  3)none of the above

2. Evaluate the definite integral f21  (x+1/x)^2 dx

a)37/6  b) 29/6   c)15/2  d)5/6   e) none of the above

Note: on question no 2.   after f sign it is 2 on the top of "f" and 1 on the bottom. I didn't knew how to use to equation editor so.

find the limit lim x to zero (sin^2 2x)/x^2 0 1 2 4 none of the above Evaluate the definite integral f21 (x+1/x)^2 dx 37/6 29/6 15/2 5/6 none of the above Note: on question no 2. after f sign it is 2 on the top of "f" and 1 on the bottom. I didn't knew how to use to equation editor so.

Explanation / Answer

lim x to zero (sin^2 2x)/x^2

using L hospital rule

sin(4x)/2x

againg differentiating it

4*cos(4x)/2

=lim x-->0 4*cos(4x)/2

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