Differentials, Errors and Approximations — Maths STD 12 Science — Question

$\triangle\text{x}=82- 81$

$=1$

Let $\text{y}=\text{x}^ {\frac{1}{4}}$

$\frac{\text{dy}} {\text{dx}}=\frac{1}{4\text{x}^{\frac{3} {4}}}$

$\Big(\frac{\text{dy}} {\text{dx}}\Big)_{\text{x}=81}=\frac{1} {4(81)^{\frac{3}{4}}}$

$=\frac{1}{108}$

$=0.009259$

$\triangle\text{y}= \Big(\frac{\text{dy}}{\text{dx}}\Big)_ {\text{x}=81}\times(\triangle\text{x})$

$=(0.0008259)(1)$

$=0.009259$

$(82)^{\frac{1}{4}}= \text{y}+ \triangle\text{y}$

$=\text {x}^\frac{1} {4}+0.009259$

$=(81)\frac{1} {4}+0.009259$

$=(81)\frac{1} {4}+3.009259$