Q. 155.0( 1 Vote )

If , find all possible values of a.

Answer :

Given,


, we need to find value of n


So we will first find the limit and then equate it with to get the value of n.


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 matches exactly with the form as described above so we don’t need to do any manipulations–


Z =


Use the formula:


Z = 9(a)9–1 = 9a8


According to question Z = = 4 + 5 = 9


9(a)8 = 9


a8 = 1 = 18 or (–1)8


Clearly on comparison we have –


a = 1 or –1


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