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# Chapter 14 - Math 4A Castroconde Worksheet 2 Chapter 14...

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Math 4A – Castroconde Name: Worksheet 2 – Chapter 14 I.D.#: Do your work on separate sheets of paper. Attach this page to your work. 1. Find 5 0 sin( ) lim 2 , , t t t t e t . 2. Find the derivative of the vector function 1 ( ) , , t r t t e t = G at t = 1. 3. Find the tangent vector to the curve defined by the vector function 2 3 ( ) , , r t t t t = G at the point corresponding to t = 1. 4. Find the unit tangent vector to the curve 2 : ( ) sin( ), 2 , C r t t t t = G at the point corresponding to t = 0. 5. The position of a particle at time t is given parametrically by 3 2 3 , 3 t t x y t = = . Show that the particle crosses the y -axis three times. 6. Evaluate 1 2 0 ˆ ˆ ( 2 ) ti t j dt 7. Let 2 ( ) 2 , sin( ), cos( ) , ( ) 1, , u t t t t v t t t = = G G . Find [ ] ( ) ( ) d u t v t dt × G G . 8. Find the points on the curve 2 3 : ( ) 2 , 12 C r t t t t t = + G where the tangent vector is horizontal or vertical. 9. Consider the curve 2 2 : ( ) , ,1 C r t t t t = G . Find the unit tangent vector, the unit normal vector, and the curvature of

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