Q9 of 61 Page 15

Using differentials, find the approximate values of the following:

Let us assume that


Also, let x = 25 so that x + Δx = 25.02


⇒ 25 + Δx = 25.02


∴ Δx = 0.02


On differentiating f(x) with respect to x, we get




We know





When x = 25, we have




Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as



Here, and Δx = 0.02


⇒ Δf = (0.1)(0.02)


∴ Δf = 0.002


Now, we have f(25.02) = f(25) + Δf



⇒ f(25.02) = 5 + 0.002


∴ f(25.02) = 5.002


Thus,


More from this chapter

All 61 →
7

The height of a cone increases by k%, its semi-vertical angle remaining the same. What is the approximate percentage increase in (i) in total surface area, and (ii) in the volume, assuming that k is small.

 8

Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius.

 9

Using differentials, find the approximate values of the following:

(0.009)1/3

 9

Using differentials, find the approximate values of the following:

(0.007)1/3