Linear approximation

Question

If the local Linear approximation of  at  is used to find the approximation for , then what is the % error of this approximation?

Answer 1

x₀ = 2 , x = 1.9

f(2) = 3sin2 + e⁶

f^'(x) = 3cosx + 3e^3x

f^'(2) = 3cos2 + 3e⁶

f(1.9) ~ L(1.9) = 3sin2 + e⁶ + (3cos2 + 3e⁶)(-.1)

Use a calculator to calculate L(1.9) and the actual f(1.9). The % error will be the difference of those values divided by f(1.9).