Skip to main content
Mathematics LibreTexts

6E: Review Excersies

  • Page ID
    31882
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Exercise \(\PageIndex{1}\)

    Evaluate the indicated limit or explain why it does not exist.

    1) \(\displaystyle \lim_{(x,y)\to(0,0)} {2\sqrt{x^2+y^2}}\)

    2) \(\displaystyle \lim_{(x,y)\to(0,0)} \frac{3x}{x^2+y^2}\)

    3) \(\displaystyle \lim_{(x,y)\to(0,0)} \frac{2\sin(xy)}{x^2+y^2}\)

    4) \(\displaystyle \lim_{(x,y)\to(0,0)} \frac{4x^2y^2}{x^2+y^4}\)

    Answer

    Add texts here. Do not delete this text first.

    Exercise \(\PageIndex{2}\)

    Define \(f(0,0)\) in a way that extends \[f(x,y)=2xy \frac{x^2-y^2}{x^2+y^2}\[ to be continuous at the origin.

    Answer

    Add texts here. Do not delete this text first.

    Exercise \(\PageIndex{3}\)

    Find the first partial derivative of \[f(x,y,z)=3x^{(y\ln z)}\[ at \((e,2,e)\).

    Answer

    Add texts here. Do not delete this text first.


    This page titled 6E: Review Excersies is shared under a not declared license and was authored, remixed, and/or curated by Pamini Thangarajah.

    • Was this article helpful?