We need to find the limit for:

As limit can’t be find out simply by putting x = 27 because it is taking indeterminate form(0/0) form, so we need to have a different approach.

Let, Z =

Using algebra of limits, we have–

Z =

⇒ Z = (27^1/3 + 3) ×

⇒ Z = 6

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 = 6

Use the formula:

∴ Z =

Hence,