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Mathematics Question on Fundamental Theorem of Calculus

Let f(x)=(x5−1)(x3+1),g(x)=(x2−1)(x2−x+1)f(x)=\left(x^{5}-1\right)\left(x^{3}+1\right), g(x)=\left(x^{2}-1\right)\left(x^{2}-x+1\right) and let h(x)h(x) be such that f(x)=g(x)h(x)f(x)=g(x) h(x). Then lim⁡x→1h(x)\displaystyle\lim _{x \rightarrow 1} h(x) is

A

0

B

1

C

3

D

5

Answer

5

Explanation

Solution

Given f(x)=g(x)h(x)f(x)=g(x) h(x)
⇒h(x)=f(x)g(x)\Rightarrow h(x)=\frac{f(x)}{g(x)}
⇒lim⁡x→1h(x)\Rightarrow \displaystyle\lim _{x \rightarrow 1} h(x)
=lim⁡x→1f(x)g(x)=\displaystyle\lim _{x \rightarrow 1} \frac{f(x)}{g(x)}