# 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

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.

Problem 7 :

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

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

## Recent Articles

1. ### Trigonometry Word Problems Worksheet with Answers

Jan 17, 22 10:45 AM

Trigonometry Word Problems Worksheet with Answers

2. ### Trigonometry Word Problems with Solutions

Jan 17, 22 10:41 AM

Trigonometry Word Problems with Solutions