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,