Problem 1 :
Let f (x) = ∛x . Find the linear approximation at x = 27. Use the linear approximation to approximate ∛27.2
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
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
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
We always appreciate your feedback.
©All rights reserved. onlinemath4all.com
Oct 30, 24 10:07 AM
Oct 29, 24 06:24 AM
Oct 29, 24 06:23 AM