Evaluate the following limits:
We need to find the limit for:
As limit can’t be find out simply by putting x = 1 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–1),we get
Z =
Using algebra of limits, we have –
Z =
Use the formula:
∴ Z =
Hence,