Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: Exercise

If $y = x^{n }$then the ratio of relative errors in$y$and $x$ is

While measuring the side of an equilateral triangle an error of $k\%$ is made, the percentage error in its area is

The circumference of a circle is measured as $28 \mathrm{cm}$ with an error of $0.01 \mathrm{cm}.$. The percentage error in the area is

If ${\log }_{e^4}=1.3868,$ then ${\log }_{e}4.01=$

The approximate value of $(33{)}^{\frac{1}{5}}$

A sphere of radius $100 \mathrm{mm}$ shrinks to radius $98 \mathrm{mm},$ then the approximate decrease in its volume is
 

If the ratio of base radius and height of a cone is $1 :2$ and percentage error in radius is$\lambda \%,$ then the error in its volume is
 

The pressure $P$ and volume $V$ of a gas are connected by the relation $P{V}^{\frac{1}{4}}=$ constant. The percentage increase in the pressure corresponding to a definition of  $\frac{1}{2} \%$in the volume is