The approximate value of (3.978)^{frac{3}{2}} | vedclass

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

Question

(A) Let $f(x) = x^{\frac{3}{2}}$.Then,$f'(x) = \frac{3}{2} x^{\frac{1}{2}}$.Using the linear approximation formula $f(a+h) \approx f(a) + h \cdot f'(a

Vedclass · Accepted Answer

$7.934$

Vedclass · Answer

(A) Let $f(x) = x^{\frac{3}{2}}$.Then,$f'(x) = \frac{3}{2} x^{\frac{1}{2}}$.Using the linear approximation formula $f(a+h) \approx f(a) + h \cdot f'(a)$,where $a = 4$ and $h = -0.022$:$f(4 - 0.022) \approx f(4) + (-0.022) \cdot f'(4)$.$f(4) = 4^{\frac{3}{2}} = (2^2)^{\frac{3}{2}} = 2^3 = 8$.$f'(4) = \frac{3}{2} \cdot 4^{\frac{1}{2}} = \frac{3}{2} \cdot 2 = 3$.Therefore,$f(3.978) \approx 8 + (-0.022) \cdot 3$.$f(3.978) \approx 8 - 0.066 = 7.934$.

The approximate value of $(3.978)^{\frac{3}{2}}$ is

Similar Questions

Let $y = f(x) = 2x^{2} - 3x + 2$. The differential of $y$ when $x$ changes from $2$ to $1.99$ is

What is an approximate value of $\sqrt{199}$ corrected to $4$ decimal places?

The approximate value of $f(x)=3x^{2}+5x+3$ at $x=3.02$ is

An approximate value of $\sqrt[4]{18}$ is

If $y = x^3 + 5$ and $x$ changes from $3$ to $2.99$,then the approximate change in $y$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module