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Application of Derivatives

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Multiple Choice Questions

391.

If f (x) = 3x² + 15x + 5, then find the approximate value of f (3.02) is

47.66
57.66
67.66
67.66

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Short Answer Type

392.

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

78 Views

393.

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

90 Views

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

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395.

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

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396.
If the radius of a sphere is measured as 7 m with an error of 0.02 m, then find the approximate error in calculating its volume.

Let r be the radius of the sphere and ∆r be the error in measuring the radius.
∴ r =7 m. ∆r = 0.02 m
Let V be volume of sphere
$therefore space space space space space space space straight V space equals space 4 over 3 πr cubed Now comma space space space space space space dV space equals space open parentheses dV over dr close parentheses increment straight r space$
$equals space 4 πr squared increment straight r space equals space 4 straight pi left parenthesis 7 right parenthesis squared space left parenthesis 0.02 right parenthesis space equals space 4 straight pi space cross times space 49 space cross times space 0.02 space equals space 3.92 space straight pi space straight m cubed$
$therefore$ approximate error in caluclating the volume = $3.92 space straight pi space straight m cubed.$

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397.

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

100 Views

398.

A circular disc of radius 3 cm is being heated. Due to expanison, its radius increases at the rate of 0.05 cm/s. Find the rate at which its area is increasing when radius is 3.2 cm.

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Multiple Choice Questions

399. The approximate change in the volume of a cube of side x metres caused by increasing the side by 3% is

0.06 x³ m³
0.6 x³ m³
0.09 x³ m³
0.09 x³ m³

81 Views

Long Answer Type

400.

If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, show that the area is maximum when the angle between them is 60°.

94 Views