Use the Linear Approximation to estimate ∆f=f(3.5)−f(3) for f(x)=2/(1+x^(2))?

Question

Δf ≈

Estimate the actual change.

(Use decimal notation. Give your answer to five decimal places.)
Δf=

Compute the error and the percentage error in the Linear Approximation.

(Use decimal notation. Give your answer to five decimal places.)

Error =

Answer 1

linear approximation means get the slope.

df/dx=-2(2x)/(1+x^2)^2

at at x=3.25, df/dt= -4*3.25/(1+3.25^2)^2=-.0972

df=-.0972*x but x= 3.5-3=.5
df=-.0488
actual

f(3)=2/(10)=1/5
f(3.5)=2/(1+3.5^2)=.150
f(3.5-f(3)=-.050

error (.0488-.050)/.050 about 2 percent
f(3.5)-f(3)=-.350

Answer 2

it says the answer is incorrect