Question

Let $f\left(x\right)=3x^{10}-7x^8+5x^6-21x^3+3x^2-7$.
The value of ${lim}_{h\to 0}\frac{f(1-h)-f\left(1\right)}{h^3+3h}$ is

• A. $\frac{50}{3}$
• B. $\frac{22}{3}$
• C. $13$
• D. None of these

Answer 1

The correct option is D None of these

Given

$f\left(x\right)=3x^{10}-7x{x}^8+5x^6-21x^3+3x^2-7$

$1=\underset{h\to 0}{lim}\frac{f(1-h)-f\left(1\right)}{-h}\times \frac{-h}{h(h^2+3)}$

$=\underset{h\to 0}{lim}f\left(1\right)\times \frac{-1}{h^2+3}$

$L=\frac{-f^1\left(1\right)}{3}$

$f^1\left(x\right)=30x^9-56x^7+30x^5-63x^2+6x$

$f^1\left(x\right)=30-56+30-63+6$

$=-53$

$L=\frac{-(-53)}{3}$

$L=\frac{53}{3}$