Errors and Approximation

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

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

Find the approximate value of

$x^3-2x^2+3x+2 \text{at} x=3.02$

Find the approximate value of

$x^4+2x^2+3 \text{at} x=2.01$

Find the approximate value correct up to four places of decimals of

${\log }_{e}9.01$ given ${\log }_{e}3=1.0986$

Find the approximate value correct up to four places of decimals of

${\log }_{e}101$ given ${\log }_{e}10=2.3026$

Find the approximate value of

$\tan \left({45}^{°},10\text{'}\right)$ given $1^{°}=0.{0175}^c$

Find the approximate value of

${\left(4.01\right)}^5$

Find the approximate value of

${\left(3.968\right)}^{\frac{3}{2}}$

Find the approximate value correct up to four places of decimals of

$\sqrt{144.02}$