Description

2 attachmentsSlide 1 of 2attachment_1attachment_1attachment_2attachment_2

Unformatted Attachment Preview

+

Breakout Room Problem #5:

Problem #5 is not from your text but will allow me to see how you can put the concepts of

Chapter 13 together to solve this problem. This problem is ” similar to” what is

demonstrated in example #3 on page 896 of your text. Create the Calcplot3D images that

displays the following descriptions:

A point moves along the path of the curve which is the intersection of the surface z = x2 +47 and the

plane y = 1.

a) Find the slope of the tangent line at (-1, 1, 5).

b) Find the equation of the tangent line at (-1,1,5)

A point moves along the path of the curve which is the intersection of the surface z = x +472 and the

planex=-1.

C) Find the slope of the tangent line at (-1, 1, 5).

d) Find the equation of the tangent line at (-1,1,5)

el Use CalcPlot3D to graph the three surfaces, the two curves of intersection, respectively, and the two

tangent lines at (-1,1,5)

Explain and Deliver:

Before I could arrive at my solution, I had to…

Here are the calculations that are outlined in the

description of my process.

896

– yoo to

Chapter 13 Functions of Several Variables

EXAMPLE 3 Finding the Slopes of a Surface

i… See Larson Calculus.com for an interactive version of this type of example.

Find the slopes in the x-direction and in the y-direction of the surface

f(x, y) =

25

at the point (1, 1, 2).

Solution The partial derivatives of f with respect to x and y are

f(x, y) = -x and f(x, y) = -2y.

Partial derivatives

So, in the x-direction, the slope is

(51)

Figure 13.30

and in the y-direction, the slope is

(1) = -2

Figure 13.31

Surface:

f(x,y)=-

-y?

100

(6.1,2)

-(1,1,2)

Slope in x-direction:

(11) —

Slope in y-direction:

(-+) –2

Figure 13.30

Figure 13.31

Purchase answer to see full

attachment

Tags:

partial derivatives

slope of the tangent

curve of intersection

slopes of surface

intersection of the surface

User generated content is uploaded by users for the purposes of learning and should be used following Studypool’s honor code & terms of service.

## Reviews, comments, and love from our customers and community:

This page is having a slideshow that uses Javascript. Your browser either doesn't support Javascript or you have it turned off. To see this page as it is meant to appear please use a Javascript enabled browser.