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

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

Question

(C) Let $f(x) = x^{3/2}$.Then,$f'(x) = \frac{3}{2} x^{1/2}$.We can write $3.978$ as $a + h$,where $a = 4$ and $h = -0.022$.Using the linear approximat

Vedclass · Accepted Answer

$7.934$

Vedclass · Answer

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

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

Similar Questions

The approximate value of $(1.0002)^{3000}$ is

If the area of a square is $575$ square units,then the approximate value of its side is

The population of a city grows at the annual rate of $3 \%$. What percentage increase is expected in $5 \text{ yr}$ (in $\%$)?

Find the approximate value of $(401)^{\frac{1}{2}}$.

The approximate value of $\log _{10} 99$ is (Given $\log _{10} e = 0.4343$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module