9.9 Small Changes and Approximations

9.9 Small Changes and Approximations


If δx is very small,  δy δx  will be a good approximation of  dy dx ,

This is very useful information in determining an approximation of the change in one variable given the small change in the second variable. 


Example:
Given that y = 3x2 + 2x – 4. Use differentiation to find the small change in y when x increases from 2 to 2.02.

Solution:
y=3 x 2 +2x4 dy dx =6x+2
The small change in y is denoted by δy while the small change in the second quantity that can be seen in the question is the x and is denoted by δx.

δy δx dy dx δy= dy dx ×δx δy=( 6x+2 )×( 2.022 )                                                                           δx=new xoriginal x δy=[ 6( 2 )+2 ]×0.02                                     Substitute x with the original value of x, i.e2. δy=0.28