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If y = sin x and x changes from to, what is the approximate change in y?

The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

A circular metal plate expands under heating so that its radius increases by k%. Find the approximate increase in the area of the plate, if the radius of the plate before heating is 10 cm.

Find the percentage error in calculating the surface area of a cubical box if an error of 1% is made in measuring the lengths of the edges of the cube.

If there is an error of 0.1% in the measurement of the radius of a sphere, find approximately the percentage error in the calculation of the volume of the sphere.

The pressure p and the volume v of a gas are connected by the relation pv^{1.4} = const. Find the percentage error in p corresponding to a decrease of in v.

The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase in (i) in total surface area, and (ii) in the volume, assuming that k is small.

Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius.

Using differentials, find the approximate values of the following:

(0.009)^{1/3}

(0.007)^{1/3}

(15)^{1/4}

(255)^{1/4}

log_{e}4.04, it being given that log_{10}4 = 0.6021 and log_{10}e = 0.4343

log_{e}10.02, it being given that log_{e}10 = 2.3026

log_{10}10.1, it being given that log_{10}e = 0.4343

cos 61°, it being given that sin 60° = 0.86603 and 1° = 0.01745 radian

(80)^{1/4}

(29)^{1/3}

(66)^{1/3}

(82)^{1/4}

(33)^{1/5}

25^{1/3}

(3.968)^{3/2}

(1.999)^{5}

Find the approximate value of f(2.01), where f(x) = 4x^{2} + 5x + 2.

Find the approximate value of f(5.001), where f(x) = x^{3} – 7x^{2} + 15.

Find the approximate value of log_{10}1005, given that log_{10}e = 0.4343.

If the radius of a sphere is measured as 9 cm with an error of 0.03 m, find the approximate error in calculating its surface area.

Find the approximate change in the surface area of cube of side x meters caused by decreasing the side by 1%.

If the radius of a sphere is measured as 7 m with an error of 0.02m, find the approximate error in calculating its volume.

Find the approximate change in the volume of a cube of side x meters caused by increasing the side by 1%.

Mark the correct alternative in the following:

If there is an error of 2% in measuring the length of a simple pendulum, then percentage error in its period is:

If there is an error of a% in measuring the edge of a cube, then percentage error in its surface is:

If an error of k% is made in measuring the radius of a sphere, then percentage error in its volume is

The height of a cylinder is equal to the radius. If an error of α% is made in the height, then percentage error in its volume is:

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

If log_{e} 4 = 1.3868, then log_{e} 4.01 =

A sphere of radius 100 mm shrinks to radius 98 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 λ%, then the error in its volume is:

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

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

The approximate value of (33)^{1/5} is

The circumference of a circle is measured as 28 cm with an error of 0.01 cm. The percentage error in the area is

For the function y = x^{2}, if x = 10 and Δx = 0.1. Find Δy.

If y = log_{e} x, then find Δy when x = 3 and Δx = 0.03.

If the relative error in measuring the radius of a circular plane is α, find the relative error measuring its area.

If the percentage error in the radius of a sphere is α, find the percentage error in its volume.

A piece of ice is in the from of a cube melts so that the percentage error in the edge of cube is a, then find the percentage error in its volume.