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Chapter 12: Multivariable Functions

1 TB.

Page 930

Intervals: What is meant by an open interval in R? What is meant by a closed interval in R? Is every interval either open or closed?

1 THINKING BACK

Page 942

Finding a direction vector for a tangent line: Find a direction vector for the line tangent to the curve \begin{equation}y=x^{3}\end{equation} when $$x = 2$$

1 THINKING FORWARD

Page 933

The derivative along a cut edge: Let

\begin{equation}f(x,y)=x^2y^3\end{equation}

Find the rate of change of f in the (positive) y direction when the surface is cut by the plane with equation x = 2. Find the rate of change of f in the (positive) x direction when the surface is cut by the plane with equation y = 1.

2 TB

Page 930

Limits: If f is a function of a single variable, what is the intuitive interpretation of limxaf(x)? What is the formal definition?

2 TB

Page 942

Finding the equation of the plane containing two intersecting lines: Show that the lines given by \begin{equation}\mathbf{r}1(t)=(3t-4,-4t+1,t) \end{equation} \begin{equation}\mathbf{r}2(t)=(-t+2,2t-9,-2t+7)\end{equation}

intersect, and find the equation of the plane containing the lines.

Q 0.

Page 903

Read the section and make your own summary of the material.

Q. 0

Page 963

Problem Zero: Read the section of Chain Rule and make your own summary of the material.

Q. 0

Page 930

Problem Zero: Read the section and make your own summary of the material.

Q. 00

Page 984

Problem Zero: Read the section and make your own summary of the material.

Q 1.

Page 915

Explain why Definition 0.1 is general enough to include functions of two and three variables.

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