Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Linear approximation a. Find the linear approximation for the following functions at the given point. b. Use part (a) to estimate the given function value. $$f(x, y)=\ln (1+x+y) ;(0,0) ; \text { estimate } f(0.1,-0.2)$$

Calculus 1 / AB

Calculus 3

Chapter 13

Functions of Several Variables

Section 7

Tangent Planes and Linear Approximation

Functions

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

04:31

A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.

12:23

In mathematics, a level set of a function f is a set of points whose images under f form a level surface, i.e. a surface such that every tangent plane to the surface at a point of the set is parallel to the level set.

02:45

Linear approximationa.…

01:57

Linear approximation a. Fi…

02:19

02:20

02:34

02:44

(a) Find the linear approx…

02:41

02:56

06:36

Compute the linear approxi…

02:35

but oppose mission. The function and thanks Why Waco Gender f x zero y zero plus f x times X minus extra plus F wife times y minus wise there are and in a question were given the function F x Why you go do the and I'm the one plus next. Plus why and upon those zero in the first time we need to find a prayer f X and f. Why now the bus Hillary respected the eggs and we go to 1/1 plus x plus y something for the F one Could 1/1 plus express why and their father Lini approximation X y Waco virtue with Buddhist phone Julia X one again a good gel and one which is there. Oh, then we have their own on F act here with Vico June 1. And, uh, we have ex miners. There are then plus, I'm going to go to one or I minus zero. And now we want to estimate the value of the function When exit could Europe on one. Why equity managers upon too. So doesn't abreast minute they go to the AM members upon one on a serpent. You so go put into this formula and we're echo. Judah is a fun one. Put miners upon to an equal to minus one.

View More Answers From This Book

Find Another Textbook

01:19

Given the following equations, evaluate dy/dx. Assume that each equation imp…

07:29

Parabolic trajectory Consider the parabolic trajectory$$x=\left(V_{0} \c…

02:57

Compute the dot product of the vectors u and $\mathbf{v},$ and find the angl…

05:52

Use Lagrange multipliers to find the maximum and minimum values of $f$ (when…

03:25

Suppose you follow the spiral path$C: x=\cos t, y=\sin t, z=t,$ for $t \…

01:50

Practical formula for N Show that the definition of the principal unit norma…

03:24

Find the radius of curvature (see Exercise 70 ) of the following curves at t…

06:15

Let $e^{x y z}=2 .$ Find $z_{x}$ and $z_{y}$ in three ways (and check for ag…

04:01

Find the volume of the following solids.(GRAPH CAN'T COPY)The solid…

02:36

Calculating orthogonal projections For the given vectors $\mathbf{u}$ and v,…