Homework SourseUse an appropriate linear approximation to estimate 3square
Use an appropriate linear approximation to estimate 3square root of 63 to 4 decimal places. Show your work.
Solution
x^3= cube,
cube root of 64= 4=x
so let
y= 3(x^3-1) = [x^3-1]^(1/3)
dy/dx= 3*x^2*[(1/3)(x^3-1)^(-2/3)]= error
63^(1/3)= 64^(1/3) - error(at x=4)
=4-0.02 = 3.98
