Find the linear approximation of the function f (x, y, z) x 3 y 2 z 2 at the point (2, 3, 4) and use it to estimate the number (1 98) 3 (3 01) 2 (3 97) 2

Question: Find the linear approximation of the function f (x, y, z) = x 3 y 2 + z 2 at the point (2, 3, 4)

Find the linear approximation of the function f (x, y, z) = x³√y² + z² at the point (2, 3, 4) and use it to estimate the number (1.98)³√(3.01)² + (3.97)².

Step by Step Solution

★★★★★

3.39 Rating (180 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

x y z x y z fxx y z 3x y z yx y z y z Yx fzx y z Zx y z so 2 3 4 ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Find the linear approximation of the function f(x) = 1 x at a = 0 and use it to approximate the numbers 0.9 and 0.9. Illustrate by graphing f and the tangent line.

Find the linear approximation of the function g(x) = 31 + x at a = 0 and use it to approximate the numbers 30.95 and 31.1. Illustrate by graphing and the tangent line.

Find the linear approximation of the function f(x) = 1 - x at a = 0 and use it to approximate the numbers 0, 9 and 0.99. Illustrate by graphing f and the tangent line.

Find the linear approximation of the function f (x, y, z) = (x 2 + y 2 + z 2 at (3, 2, 6) and use it to approximate the number (3.02) 2 + (1.97) 2 + (5.99) 2 .

- Long Answer Questions er Questions Find the linear approximation to the function f (x, y) = 31 + 3ry at the point (z, y) = (3, -3) L (2, y) = ab va a sin (a) (write the appropriate function of z...

Please show work - Long Answer Questions er Questions Find the linear approximation to the function f (x, y) = 31 + 3ry at the point (z, y) = (3, -3) L (2, y) = ab va a sin (a) (write the appropriate...

Question . 1 Consider the surface x + + Using a graphing tool . to sketch this Surface . Then . answer the following a ) . Find the equation of the tangent plane to this surface at the point (312, 2...

For 1-5 IE ll! 5. Find the linear approximation of the function f (x) = '11 - x at a = 0 and use it to approximate the numbers 0.9 and 0.99. Illustrate by graphing f and the 2. f(x) = 23*, a = 0...

compute the linear approximation of the function f ( x , y ) = z x 2 about the point ( xo, 4). use the result to estimate the value of Flats

Find the linear approximation of the function f x 1 x at a 0 L x Use L x to approximate the numbers 0 9 and 0 99 Round your answers to four decimal places 0 9 0 99 Illustrate by graphing f and the...

(Lau You are considering buying a piece of land priced today at $400,000. The bank has offered you a loan to buy it. The loan is a 10-year loan for which you will make semi-annual payments (at the...

Explain how UPSs job design is affected by its mission to be environmentally conscious.

g . Construct an example showing that the hedge works. Make sure the example illustrates how the hedge portfolio earns the risk - free rate over both periods. h . What would an investor do if the...

However, it generally is agreed that the effect is more important for dividends than it is for capital structure. EMPIRICAL TESTING AND IMPLICATIONS FOR PAYOUT While we have seen that a number of...

A lab has a culture of a new kind of bacteria where each individual takes 2 hours to split into three bacteria. Suppose that these bacteria never die and that all offspring are OK. a. Write an...

The number of bacteria (in millions) in a lab are as follows Time, t (h)Number, bt 0.0 ........................1.5 1.0 ........................3.0 2.0 ........................4.5 3.0...

The number of bacteria in another lab follows the discrete-time dynamical system where t is measured in hours and bt in millions of bacteria. a. Graph the updating function. For what values of bt...

StatCrunch Assignment 1A You will select a sample of 100 students from this population and analyze the data from the sample to draw conclusions about the entire population. We want our sample to be...

1.Find the point estimate of the population mean and the margin of error for a 90% confidence interval for the following drive times (in minutes) for commuters to a college. 354047221719364465...

Your division is considering two projects with the following cash flows (in millions): a. What are the projects' NPVs assuming the WACC is 5% ? Enter your answer in millions. For example, an answer...