Using differentiation,the approximate value of $f(x) = x^2 - 2x + 1$ at $x = 2.99$ is ....

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

If an error of $0.02 \text{ cm}^2$ is found in the surface area of a sphere when its radius is measured as $10 \text{ cm}$, then the approximate error that occurs in the volume of the sphere, in cubic centimetres, is

By considering $1^{\prime} = 0.0175$ radians,the approximate value of $\cot 45^{\circ} 2^{\prime}$ is

The approximate value of $3^{2.001}$,given that $\log 3 = 1.0986$,is

The time period $T$ of a simple pendulum of length $l$ is given by $T=2 \pi \sqrt{\frac{l}{g}}$. If the length is increased by $2 \%$, then the approximate change in the time period is: