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lecture #21. Review for Test 2

# lecture #21. Review for Test 2 - Math 234 SS 2008 Review...

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Math 234 SS 2008 Review for Test 2 . CH 13.1, 13.3, 14.1-14.6. Test 2 covered material from CH 13.1, 13.3; CH 14.1-14.6. Outlines for Test 2. 1. Position vector. Velocity, speed, acceleration of a particle moving in space. 2. Tangent line to a curve (parametric equations). 3. Arc length parameter with the given base point. Unit Tangent Vector. 4. Domain, range of a function of several variables. Open/closed regions. Bounded/unbounded regions. 5. Level curve. Level surface. Finding the equation of the level curve that passes through a given point. 6. Two-path Test for Nonexistence of a limit. (like example #5 p. 980). 7. Partial derivatives. Chain rule. Using tree diagrams to find partial derivatives for different combinations of intermediate and independent variables. 8. Implicit differentiation. (p.1002). 9. Directional derivatives. Gradient vectors. 10. Equation for the plane tangent to the surface (line tangent to the curve). 11. Linearization. Standard Linear Approximation. The Error in the Standard Linear Approximation (Examples 5-6 pp.1019-1020). 1

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Math 234 SS 2008 Review for Test 2 . CH 13.1, 13.3, 14.1-14.6. I. Vector-Valued Functions. 1. ( 29 ( 29 2 4 3 7 3 t t t t = - + - r i j k is the position vector of a particle in space at time t . a) Find the particle’s velocity and acceleration. b) Find the particle’s speed and direction of motion at 1 t = .
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