Answer :

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 =

Dividing numerator and denominator by (x–a),we get

Z =

Using algebra of limits, we have –

Z =

Use the formula:

∴ Z =

Hence,

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