PRACTICE PROBLEMS WITH LINEAR APPROXIMATION

Problem 1 :

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

Solution

Problem 2 :

Use the linear approximation to find approximate values of

(i)  (123)^2/3

(ii)  (15)^1/4

(iii)  ∛26              Solution

Problem 3 :

(i)  f(x)  =  x³-5x+12 and x₀  =  2

(ii)  g(x)  =  √(x²+9) and x₀  =  -4

(iii)  h(x)  =  x/(x+1) and x₀  =  1

Solution

Problem 4 :

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:

(i) Absolute error (ii) Relative error (iii) Percentage error

Solution

Problem 5 :

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 :

(i) change in the volume (ii) change in the surface area

Solution

Problem 6 :

The time T , taken for a complete oscillation of a single pendulum with length l , is given by the equation

T  =  2π√(l/g)

where g is constant. Find the approximate percentage error in the calculated value of T corresponding to an error of 2 percent in the value of 1.

Solution

Problem 7 :

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

Solution

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