Question

A) Use the Linear Approximation to estimate Δ* f*
=

Δ* f* ≈

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.)

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:

Find the linear approximation of the function f(x, y, z) = x2 +
y2 + z2 at (6, 2, 9) and use it to approximate the number 6.012 +
1.972 + 8.982 . (Round your answer to five decimal places.) f(6.01,
1.97, 8.98) ≈

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 both the local linear and local quadratic approximation to
estimate f(0.1, −0.1) where f(x, y) = cos(x + y)e x−y .

Use Linear Approximation to estimate
Δ?=?(13.02)−?(13) for
?(?)=?^4.
(Use decimal notation. Give your answer to two decimal
places.)

Hint if need to find ex 4.1^5 make f(x)= x^5, f'(x)= 5x^4, and
plug in 4 to f(x), f'(x), and f''(x) to use the quadratic
approximation Find f(x), f' (x), and f'' (x) to use the quadratic
approximation
Show step by step to understand.
1.Use quadratic approximation to...
a.to estimate √66 ^3 to 3 decimal places if possible.
b. to estimate ??? 46 degrees to 3 decimal places if
possible.
c. to estimate ??? 89 degrees to 3 decimal places...

Consider the function f(x)= squareroot of (3x)
1) find the linear approximation to the function f at a=4
2) use the linear approximation from part 1 to estimate
squareroot of (12.6)

-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)

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.

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

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