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

Let f(x) = `root(3)(x)`. Find the linear approximation at x = 27. Use the linear approximation to approximate `root(3)(27.2)`

Use the linear approximation to find approximate values of `(123)^(2/3)`

Use the linear approximation to find approximate values of `root(4)(15)`

Use the linear approximation to find approximate values of `root(3)(26)`

Find a linear approximation for the following functions at the indicated points.

f(x) = x³ – 5x + 12, x₀ = 2

Find a linear approximation for the following functions at the indicated points.

g(x) = `sqrt(x^2 + 9)`,  x₀ = – 4

Find a linear approximation for the following functions at the indicated points.

h(x) = `x/(x + 1), x_0` = 1

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Absolute error

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Relative error

The radius of a circular plate is measured as 12.65 cm instead of the actual length 12.5 cm. find the following in calculating the area of the circular plate:

Percentage error

A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:

Change in the volume

A sphere is made of ice having radius 10 cm. Its radius decreases from 10 cm to 9.8 cm. Find approximations for the following:

Change in the surface area

The time T, taken for a complete oscillation of a single pendulum with length l, is given by the equation T = `2pi sqrt(l/g)` where g is a constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of l

Show that the percentage error in the n^th root of a number is approximately `1/"n"` times the percentage error in the number

Find the differential dy for the following functions:

y = `(1 - 2x)^3/(3 - 4x)`

Find the differential dy for the following functions:

y = `(3 + sin(2x))^(2/3)`

Find the differential dy for the following functions:

y = `"e"^(x^2 - 5x + 7) cos(x^2 - 1)`

Find df for f(x) = x² + 3x and evaluate it for x = 2 and dx = 0.1

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