If displaystylelim-xrightarrow 3-dfrac-x-n-3-n-x-3-108- the value of n-

Question

Toppr Admin · Accepted Answer

Correct option is A- 4Using formula -displaystyle -lim-x-rightarrow a-dfrac-x-n-a-n-x-a-n-a-n-1-displaystyle -lim-x-rightarrow 3-dfrac-x-n-3-n-x-3-n-3-4-1-4-3-3-n-4-

If $$\displaystyle\lim_{x\rightarrow 3}\dfrac{x^n-3^n}{x-3}=108$$, find the value of n.

Correct option is A. 4

Using formula $$\displaystyle \lim_{x\rightarrow a}{\dfrac{x^n-a^n}{x-a}}=n.a^{n-1}$$

$$\displaystyle \lim_{x\rightarrow 3}{\dfrac{x^n-3^n}{x-3}}=n.3^{4-1}=4.3^3$$

$$n=4$$

If $$\displaystyle\lim_{x\rightarrow 3}\dfrac{x^n-3^n}{x-3}=108$$, find the value of n.

Correct option is A. 4Using formula $$\displaystyle \lim_{x\rightarrow a}{\dfrac{x^n-a^n}{x-a}}=n.a^{n-1}$$$$\displaystyle \lim_{x\rightarrow 3}{\dfrac{x^n-3^n}{x-3}}=n.3^{4-1}=4.3^3$$$$n=4$$

Correct option is A. 4

Using formula $$\displaystyle \lim_{x\rightarrow a}{\dfrac{x^n-a^n}{x-a}}=n.a^{n-1}$$

$$\displaystyle \lim_{x\rightarrow 3}{\dfrac{x^n-3^n}{x-3}}=n.3^{4-1}=4.3^3$$

$$n=4$$