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

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= 3.53=.5
df=.0488
actual
f(3)=2/(10)=1/5
f(3.5)=2/(1+3.5^2)=.150
f(3.5f(3)=.050
error (.0488.050)/.050 about 2 percent
f(3.5)f(3)=.350 
it says the answer is incorrect
Respond to this Question
Similar Questions

Calculus
Estimate delta(x) using the Linear Approximation and use a calculator to compute both the error and the percentage error. f(x)=cosx a=(pi/4) delta(x)=.06 delta(x)= ______ i got this part and it's .04242 The error in Linear Approximation … 
math
(a) Use the Midpoint Rule and the given data to estimate the value of the integral I. (Give the answer to two decimal places.) I = int_0^3.2 f(x)dx 1 x f(x) x f(x) 0.0 7.3 2.0 8.8 0.4 6.8 2.4 7.3 0.8 8.1 2.8 7.6 1.2 7.6 3.2 7.3 1.6 … 
Calculus
Estimate delta f using the Linear Approximation and use a calculator to compute the error. f(x)=sqrt(3+x). a=6. delta x=0.1. delta f= With these calculations, we have determined that the square root of ___________ is approximately … 
calculus
The radius of a sphere was measured to be cm with a possible error of cm. Use linear approximation to estimate the maximum error in the calculated surface area. Leave your answer in terms of . Use linear approximation to estimate the … 
calculus
The circumference of a sphere was measured to be 74 cm with a possible error of 0.5 cm. (a) Use differentials to estimate the maximum error in the calculated surface area. (Round your answer to the nearest integer.) cm2 What is the … 
Practice Exam Calculus
The radius of a sphere was measured to be 20cm with a a possible error of 1/5cm 1).Use linear approximation to estimate the maximum error in the calculated surface area. Leave your answer in terms of pi. 2).Use linear approximation … 
Calculus Help Please!!!
Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = 3x − x^2, x = 3, Δx = −0.6 Δy=? 
Calculus Help Please!!!
Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) ln(1 … 
Math
The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated surface … 
Calculus
The measurement of the side of a square is found to be 12 cm with a possible error of 0.05 cm. Use differentials to estimate the propagated error ΔA in computing the area of the square. Please do not include the ± symbol in your …