Question

Use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (Round your answers to four decimal places.)

3

26

Answer 1

Let's assume that we have,

we can write,

we know that differential approximation of a function y = f(x) at x = a is given by,

we can write,

   ----------------------------------------------------------1)

we have,

Hence,

Put this value in equation 1) we can write,

   -------------------------------------------------2)

we have,

Hence,

Hence,

Put this value in equation 2) we can write,

we have,

Hence we can write,

rounding to 4 decimal places we can say that,

using calculator we can write,

rounding to 4 decimal places we can say that,

which is almost equal as we have found above