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Chapter 12: Multivariable Functions

Expert-verified
Calculus
Pages: 903 - 990
Calculus

Calculus

Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

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Illustration

624 Questions for Chapter 12: Multivariable Functions

  1. 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?

    Found on Page 930

  2. 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 $$x = 2$$

    Found on Page 942

  3. The derivative along a cut edge: Let

    Found on Page 933

  4. Limits: If f is a function of a single variable, what is the intuitive interpretation of limx→af(x)? What is the formal definition?

    Found on Page 930

  5. 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}

    Found on Page 942

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

    Found on Page 903

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

    Found on Page 963

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

    Found on Page 930

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

    Found on Page 984

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

    Found on Page 915

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