The approximate value of sqrt[5]{33} correct | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $f(x) = x^{1/5}$. We need to find the value of $f(33)$.Let $x = 32$ and $\Delta x = 1$,so that $x + \Delta x = 33$.We know that $f(x) = x^{1/5

Vedclass · Accepted Answer

$2.0125$

Vedclass · Answer

(C) Let $f(x) = x^{1/5}$. We need to find the value of $f(33)$.Let $x = 32$ and $\Delta x = 1$,so that $x + \Delta x = 33$.We know that $f(x) = x^{1/5} \implies f'(x) = \frac{1}{5} x^{-4/5} = \frac{1}{5 x^{4/5}}$.At $x = 32$,$f(32) = (32)^{1/5} = 2$.$f'(32) = \frac{1}{5(32)^{4/5}} = \frac{1}{5(2^4)} = \frac{1}{5 	imes 16} = \frac{1}{80} = 0.0125$.Using the differential approximation formula: $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$.$f(33) \approx f(32) + f'(32) 	imes 1$.$f(33) \approx 2 + 0.0125 = 2.0125$.

The approximate value of $\sqrt[5]{33}$ correct to $4$ decimal places is

Similar Questions

The approximate value of $f(x)=x^3+5x^2-7x+9$ at $x=1.1$ is

By considering $1^{\prime} = 0.0175$ radians,the approximate value of $\cot 45^{\circ} 2^{\prime}$ is

Find the approximate value of $(3.968)^{\frac{3}{2}}$.

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing the side by $2 \%$.

The approximate value of $\sin 31^{\circ}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module