Question

Use linear approximation to estimate the following quantity. Choose a value of a to produce a small error.

**Question:** 3√9 = ??

3 square root 9 = ?

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:

Use Linear Approximation to estimate the increase in volume of a
cube whose side increases from 1 inch to 1.064 inches. DO NOT
calculate this quantity directly.

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.

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

Notice that ln(20) is slightly less than 3? Use a linear
approximation to estimate f(3)=e^3 using the fact that e^ln(20) =
20

Complete steps (i)-(vii) below in order to estimate the
following values using linear approximation: (a) cos(31π/ 180) (i)
Identify the function, f(x). (ii) Find the nearby value where the
function can be easily calculated, x = a. (iii) Find ∆x = dx. (iv)
Find the linear approximation, L(x). (v) Compute the approximate
value of the expression using the linear approximation. (vi)
Compare the approximated value to the value given by your
calculator. (vii) Compare dy and ∆y using the value...

Using the linear approximation system to estimate the profit
maximizing price requires that the managers know the costs of
production and
the production function
one price and quantity of demand
two prices and quantities of demand
decision-making process of the marketplace

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.

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 .

-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)

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