Question

Assume that 1+2x is the linear approximation for sqrt(1+4x) near x = 0. Use it to approximate sqrt(0.76) and then compute the absolute error and relative error of this approximation.

Answer #1

Estimate ΔfΔf using the Linear Approximation and use a
calculator to compute both the error and the percentage
error.
f(x)=sqrt(19+x) .a=6.Δx=−0.5
With these calculations, we have determined that the square root
is approximately
The error in Linear Approximation is:
The error in percentage terms is:

1.
The linearization of f(x)=(e^x^2) at x=1 is?
2. The linear approximation of f(x)=sqrt(x+3) is?
3. compute the average value of f(x)=(x^3)+(3x^2) over
interval [1,2] is?

Find the linear approximation of the function f(x, y, z) = sqrt
x2 + y2 + z2 at (3, 6, 6) and use it to approximate the number
sqrt3.01^2 + 5.97^2 + 5.98^2 . (Round your answer to five decimal
places.) f(3.01, 5.97, 5.98)

Use linear approximation to find a linear representation for ?
= √1 + 3? ?? ? = 1 and use this result to evaluate √3.99. Also find
the percent relative error in this problem.

A) Use the Linear Approximation to estimate Δf
= f(4.9) − f(5) for
f(x) = x −
6x2.
Δf ≈
B)Estimate the actual change.
Δf =
C)Compute the error in the Linear Approximation
D)Compute the percentage error in the Linear Approximation.
(Round your answer to five decimal places.)

2-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.)
1
(1 + 4x)4
≈ 1 − 16x

Use zero to third order approximations, respectively to
determine f(x) = (4x - 6)3
using base point xi = 2 by Taylor series
expansion. Approximate f(4) and compute true percent
relative error |εt| for each approximation.

-find the differential and linear approximation of f(x,y) =
sqrt(x^2+y^3) at the point (1,2)
-use tge differential to estimate f(1.04,1.98)

1) which of the following is a linear approximation of the
function f(x)= sqrt[ 4 ] { x } at a=16.
2) determine the number of inflection points on the graph of
the function f(x)=x^5-x^4.
3) determine the sum of the critical numbers for the function
f(x)=x^3+3x^2-9x.

Find the linear approximation L(x) to y = xsinx for values of x
near a = π

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 32 minutes ago

asked 34 minutes ago

asked 45 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago