Q. 13

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Given, , we need to find value of n

So we will first find the limit and then equate it with 9 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 = 9

9(a)8 = 9

a8 = 1 = 18 or (–1)8

Clearly on comparison we have –

a = 1 or –1

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