Q. 9 I

# Using differentials, find the approximate values of the following:loge10.02, it being given that loge10 = 2.3026

loge10.02, it being given that loge10 = 2.3026

Let us assume that f(x) = logex

Also, let x = 10 so that x + Δx = 10.02

10 + Δx = 10.02

Δx = 0.02

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

We know

When x = 10, 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(10.02) = f(10) + Δf

f(10.02) = loge10 + 0.002

f(10.02) = 2.3026 + 0.002

f(10.02) = 2.3046

Thus, loge10.02 ≈ 2.3046

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Human Evolution | An Important Concept40 mins
Medelian disorder series: Thalassemia, Sickle cell anaemia & Phenylketonuria60 mins
Interactive Quiz | Biotechnology - 0342 mins
Human Evolution38 mins
Rapid Quiz challenge - Cell Structure & Cell Division52 mins
Different high order thinking questions based on DNA structure39 mins