Q. 74.2( 10 Votes )

Evaluate the following limits:


Answer :

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 = (271/3 + 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,


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