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Ch 4.7 Wkst AP Calc BC Name:
Parametric Equations Day 1
For parametric equations, [pic], the first derivative is [pic] and the second derivative is [pic] .
For problems #1-4, find a) [pic] and b) [pic].
1. [pic] , [pic]
2. [pic] , [pic]
3. [pic] , [pic]
4. [pic] , [pic]
For problems #5-7, find the equation of the tangent line at the indicated value(s).
5. [pic] , [pic] at t = 1
6. [pic] , [pic] at t = π
7. [pic] , [pic] at ( -2 , 2)
8. A curve described by the parametric equations [pic] and [pic] is concave up over what interval(s)?
9. At time t , the position of a particle moving on a curve is given by [pic] and [pic].
a) Find [pic].
b) Find all values of t at which the curve has
i) a horizontal tangent
ii) a vertical tangent
c) Find the horizontal asymptotes of [pic].
10. An object moves along the path [pic] and [pic], where t is time.
a) Write an equation for the line tangent to this path at [pic].
b) Find the smallest positive value of t for which the y-coordinate is a local maximum.
c) What is the concavity of the graph at t = 2?
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ANSWERS:
1) [pic] 4) [pic] 7) [pic] 9a) [pic] 10a) [pic]
2) j©K¥][pic]hôeðU[pic]V[pic]h¦%ÂhôeðCJEHæÿU[pic]j§K¥][pic]hôeðU[pic]V[pic]h¦%ÂCJ EMBED Equation.3 [pic] 5) [pic] 8) [pic] b) none ,[pic] b) π
3) [pic] 6) [pic] c) [pic] c) Up, since [pic]
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