HSC Science Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Find df for f(x) = x² + 3x and evaluate it for x = 3 and dx = 0.02

Find Δf and df for the function f for the indicated values of x, Δx and compare:

f(x) = x³ – 2x², x = 2, Δx = dx = 0.5

Find Δf and df for the function f for the indicated values of x, Δx and compare:

f(x) = x² + 2x + 3, x = – 0.5, Δx = dx = 0.1

Assuming log₁₀ e = 0.4343, find an approximate value of Iog₁₀ 1003

The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. Approximately how much did the tree diameter grow?

The trunk of a tree has a diameter of 30 cm. During the following year, the circumference grew 6 cm. What is the percentage increase in the area of the cross-section of the tree?

An egg of a particular bird is very nearly spherical. If the radius to the inside of the shell is 5 mm and the radius to the outside of the shell is 5.3 mm, find the volume of the shell approximately

Assume that the cross-section of the artery of human is circular. A drug is given to a patient to dilate his arteries. If the radius of an artery is increased from 2 mm to 2.1 mm, how much is cross-sectional area increased approximately?

In a newly developed city, it is estimated that the voting population (in thousands) will increase according to V(t) = 30 + 12t² – t³, 0 ≤ t ≤ 8 where t is the time in years. Find the approximate change in voters for the time change from 4 to `4 1/6` years

The relation between the number of words y a person learns in x hours is given by y = `sqrt(x), 0 ≤ x ≤ 9`. What is the approximate number of words learned when x changes from 1 to 1.1 hours?

The relation between the number of words y a person learns in x hours is given by y = `sqrt(x), 0 ≤ x ≤ 9`. What is the approximate number of words learned when x changes from 4 to 4.1 hours?

A circular plate expands uniformly under the influence of heat. If its radius increases from 10.5 cm to 10.75 cm, then find an approximate change in the area and the approximate percentage change in the area

A coat of paint of thickness 0.2 cm is applied to the faces of cube whose edge is 10 cm. Use the differentials to find approximately how many cubic centimeters of paint is used to paint this cube. Also calculate the exact amount of paint used to paint this cube

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A circular template has a radius of 10 cm. The measurement of the radius has an approximate error of 0.02 cm. Then the percentage error in the calculating the area of this template is

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The percentage error of fifth root of 31 is approximately how many times the percentage error in 31?

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If u(x, y) = `"e"^(x^2 + y^2)`, then `(delu)/(delx)` is equal to

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If we measure the side of a cube to be 4 cm with an error of 0.1 cm, then the error in our calculation of the volume is

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The change in the surface area S = 6x² of a cube when the edge length varies from x₀ to x₀ + dx is

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The approximate change in volume V of a cube of side x meters caused by increasing the side by 1% is

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If f(x) = `x/(x + 1)`, then its differential is given by