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