Math 252 Review Sheet:

1. Review the followings if

1. the arc length of

2. the unit tangent vector,

3. the unit normal vector,

4. the unit binormal vector,

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 and

2. Consider the space curve

1. Find the tangent line when

2. Set up the integral for the arc length of for to

3. Use Maple to figure out and

3. Repeat problem 2 above if

4. Consider the space curve

1. Sketch the curve from to

2. Draw the vectors and

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

5. Use implicit differentiation to find the curvature of an ellipse at and

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

7. The existence of a limit

1. Review examples from your notes and homeworks.

2. Determine if exists.

3. Find the limit if it exists:

8. Find the region where is continuous.

9. Find the region where is continuous.

10. Understanding Partial Derivatives algebraically and graphically.

1. Consider

1. find

2. If is the curve traveling traveling along from to find the parameterization for

3. explain the relationship between and

2. Try the homworks from the text.

3. Use Maple to understand partial derivatives graphically.

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