Share
Notifications

View all notifications

Approximations

Login
Create free account


      Forgot password?

notes

Let f : D → R, D ⊂ R, be a given function and let y = f(x).  Let ∆x denote a small increment in x. Recall that the increment in y corresponding to the increment in x, denoted by ∆y, is given by ∆y = f(x + ∆x) – f(x). Fig. 
We define the following 

(i) The differential of x, denoted by dx, is defined by dx = ∆x. 

(ii) The differential of y, denoted by dy, is defined by dy = f′(x) dx or
`dy =((dy)/(dx)) triangle x . `

In case dx = ∆x is relatively small when compared with x, dy is a good approximation of ∆y and we denote it by dy ≈ ∆y.
For geometrical meaning of  ∆x, ∆y,  dx and  dy, one may refer to Fig.

Video link : https://youtu.be/5NxtGK0Bs-U

Video Tutorials

We have provided more than 1 series of video tutorials for some topics to help you get a better understanding of the topic.

Series 1


Series 2


Shaalaa.com | Application of Derivatives part 16 (Approximation)

Shaalaa.com


Next video


Shaalaa.com


Application of Derivatives part 16 (Approximation) [00:12:47]
S
Series 2: playing of 2
2
0%


S
View in app×