Q. 64.8( 4 Votes )

Evaluate the following limits:


Answer :

We need to find the limit for:


As limit can’t be find out simply by putting x = (–1/2) because it is taking indeterminate form(0/0) form, so we need to have a different approach.


Let, Z =


Z =


Note: To solve the problems of limit similar to one in our question we use the formula mentioned below which can be derived using binomial theorem.


Formula to be used:


As Z matches exactly with the form as described above so we don’t need to do any manipulations–


Z =


Let y = 2x


As x 1/2 2x = y –1


Z =


Use the formula:


Z =


Hence,


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