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) = x^{3}-5x+12 and x_{0} = 2
(ii) g(x) = √(x^{2}+9) and x_{0} = -4
(iii) h(x) = x/(x+1) and x_{0} = 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 n^{th} root of a number is approximately 1/n times the percentage error in the number.
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