Evaluate the following limits:

We need to find the limit for:


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


Let, 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 does not match exactly with the form as described above so we need to do some manipulations–


Z =


Z =


Let x + 2 = y and a+2 = k


As x a ; y k


Z =


Use the formula:


Z =


Hence,


2