Errors and Approximations

Using differentials, the approximate value of ${\left(82\right)}^{\frac{1}{4}}$ upto $3$ places of decimal would be

If an error of $0.02 \mathrm{sq}.\mathrm{cm}$ is found in the surface area of a sphere when its radius is measured as $10 \mathrm{cm}$, then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is

If the error committed in measuring the radius of the circle is $0.05\%$, then the corresponding error in calculating the area is

The approximate value of $5^{2.01}$ is $\dots \dots \dots$, where, $\left({\log }_{e}5=1.6095\right)$.

Use differential to approximate $\sqrt{36.6}$.

Find the approximate value of

$e^{1.002}$ given $e=2.7183$

Find the approximate value of

${\sin }^{-1}\left(0.51\right)$ given $\sqrt{3}=1.7321$

Find the approximate value of

$\sin \left({60}^{°},0^{\text{'}},{10}^{\text{'}\text{'}}\right)$ given $1^{°}=0.{0175}^c$

Find the approximate value of

$\sqrt[3]{26.96}$

If the radius af a sphere is measured as $7 cm$ with an error of $0.01 cm$, then the approximate error is calculating the volume is (use $\pi =\frac{22}{7}$)

Find the approximate change in the volume $V$ of a cube of side $x$ meters caused by increasing side by $2\%$.

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

The approximate value of the function $f\left(x\right)=x^3-3x+5$ at $x=1.99$ is

If the error in measuring the side $l$ of an equilateral triangle is $0.01\mathrm{cm}$, then the percentage error in the area of the triangle, in terms of its side $l$ is

The angle $A$ of $\Delta ABC$ is found by measurement to be $67\frac{1}{2}°$ and the area of $\Delta ABC$ is calculated from the measurements of $b,c,A.$ In measuring $A,$ an error of $9$ minutes is made, then the percentage error in the area of the triangle is

If the edge of a cube is measured with an error of $5\%$, then find the approximate error to calculate its volume.

If the radius of a sphere decreases from $10$ cm to $9.8$ cm, find the approximate error in calculating its volume.