Answer :

Let us assume that f(x) = x5


Also, let x = 2 so that x + Δx = 1.999


2 + Δx = 1.999


Δx = –0.001


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



We know




When x = 2, 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 = –0.001


Δf = (80)(–0.001)


Δf = –0.08


Now, we have f(1.999) = f(2) + Δf


f(1.999) = 25 – 0.08


f(1.999) = 32 0.08


f(1.999) = 31.92


Thus, (1.999)5 ≈ 31.92


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
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
caricature
view all courses
RELATED QUESTIONS :

If y = sin x and RD Sharma - Volume 1

Find the percentaRD Sharma - Volume 1

A circular metal RD Sharma - Volume 1

The radius of a sRD Sharma - Volume 1

The height of a cRD Sharma - Volume 1

Find the approximMathematics - Exemplar

Find the point onMathematics - Board Papers