Question

Lim. x^n - 3^n÷x-3 =108,find n
x tends to 3

Answer 1

The value of n is 4.

Step-by-step explanation:

The given problem is

$lim_{x\rightarrow 3}\dfrac{x^n-3^n}{x-3}=108$

We know that, for any positive integer n

$lim_{x\rightarrow a}\dfrac{x^n-a^n}{a-3}=na^{n-1}$

After applying limit in the given equation, we get

$n(3)^{n-1}=108$

$n(3)^{n-1}=4\times 27$

$n(3)^{n-1}=4\times 3^3$

$n(3)^{n-1}=4\times 3^{4-1}$

On comparing both sides we get

$n=4$

Therefore, the value of n is 4.

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