# Evaluate the following limits:

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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