Use the linear approximation to estimate 09832032 Compare wi

Use the linear approximation to estimate

(0.98)^3(2.03)^2

Compare with the value given by a calculator and compute the percentage error:
Error = %

The function is a type of cubic terms let us seperate the two terms (-0.98)^3 and (-2.03)^2

f(x) = x^3 where for x=-1 and f(-1) = -1

f(-0.98) = f(-1) + f\'(-1) * (-0.98-(-1))

f(-0.98) = -1 + 3(-1)^2 * 0.02 = -1 + 0.06 = -0.94

Similarly second part can be approximated as

f(y) = y^2

f(-2) = 4

f(-2.03) = f(-2) + f\'(-2) * (-2.03+2)

=> 4 -4*(0.03)

=> 4.12

Hence the linear approximation value is -0.94* 4.12 = 3.8728

and actual value by calculator is 3.87855

Percentage Error = (3.87855 - 3.8728)/3.8728 * 100 = 0.15%