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  Everything About Genetic DisordersFREE Class  Meselson and Stahl experiment49 mins  Interactive Quiz on Human Evolution33 mins  Application of Biotechnology | Concepts - 0256 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 