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

If $y=5x^2+6x+6$,$x=2$,and $\Delta x=0.001$,then the values of $\Delta y$ and $dy$ respectively are:

If $1^{\circ} = \alpha$ radians,then the approximate value of $\cos(60^{\circ} 1^{\prime})$ is

The approximate value of $\log _{10} 998$ is (given that $\log _{10} e=0.4343$ )

The approximate value of $\cot ^{-1}(1.001)$ is

If the percentage error in the radius of a circle is $3\%$, then the percentage error in its area is (in $\%$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module