Math 252 Review Sheet:

  1. Review the followings if MATH

    1. the arc length of MATH

    2. the unit tangent vector, $T(t);$

    3. the unit normal vector, $N(t);$

    4. the unit binormal vector, $B(t);$

    5. the curvature function, (theorem 9,10 and 11)

    6. the velocity function,

    7. the acceleration function.

    8. express the acceleration function in terms of $T(t)$ and $N(t).$

  2. Consider the space curve MATH

    1. Find the tangent line when $t=1.$

    2. Set up the integral for the arc length of MATH for $t=0$ to $t=1.$

    3. Use Maple to figure out $T(t),N(t)$ and $B(t).$

  3. Repeat problem 2 above if MATH

  4. Consider the space curve MATH

    1. Sketch the curve from $t=0$ to $t=2\pi .$

    2. Draw the vectors MATH and MATH

    3. Indicate where the curvature for MATH is the largest and the smallest (by inspection) for MATH

  5. Use implicit differentiation to find the curvature of an ellipse MATH at $(\pm a,0)$ and $(0,\pm b).$

  6. Understanding the contour map and the level curves. For example:

    1. $f(x,y)=x^{2}-y$

    2. $f(x,y)=3x-y$

    3. $f(x,y)=x^{2}-y^{2}$

  7. The existence of a limit MATH

    1. Review examples from your notes and homeworks.

    2. Determine if MATH exists.

    3. Find the limit if it exists: MATH

  8. Find the region where MATH is continuous.

  9. Find the region where MATH is continuous.

  10. Understanding Partial Derivatives algebraically and graphically.

    1. Consider MATH

      1. find $f_{x}(x,y),$

      2. If MATH is the curve traveling traveling along $f(x,0)$ from $x=1$ to $x=-1,$ find the parameterization for MATH

      3. explain the relationship between MATH and $f_{x}(x,0)$

    2. Try the homworks from the text.

    3. Use Maple to understand partial derivatives graphically.

This document created by Scientific WorkPlace 4.0.