wiz-icon
MyQuestionIcon
MyQuestionIcon
4
You visited us 4 times! Enjoying our articles? Unlock Full Access!
Question

Using differentials, find the approximate value of (1781)14

Open in App
Solution

Here we will assume a function f(x)=x14
Formula for approximation is given by
f(x+x)=f(x)+f(x).x
f(x)=14(x)34
Now most important step is to find x and for this we need to refer to question.
We need to choose x and one important thing which we need to keep in mind is that x when inserted in f(x) should give a perfect outcome, here x should be the nearest number to 1781 and should give a perfect fourth root.
Best number which can be seen is 1681 so from here we can conclude that x=181
Plugging all the value in formula f(x+x)=f(x)+f(x).x
We get (1681)14+ 14(1681)34.181
This is equal to 6596.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Rate of Change
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon