HW3MATH53S18.pdf - HW#3 Date Math 53 Multivariable Calculus...

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HW #3; Date: 1/22/2018Math 53 Multivariable Calculuswith Professor StankovaJanuary 26, 20181Problem Set 10.2Calculus with Parametric Curves2. Finddydx:x=tet, y=t+ sint.We use our formula (based on the chain rule) fordydxfor parametric curves:dydx=dydtdxdt=(t+ sint)0(tet)0=1 + costtet+et.6. Find an equation of the tangent to the curvex=etsinπt, y=e2t, t= 0 at the point wheret= 0.
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8. Find an equation of the tangent tox= 1+t, y=et2at the point (2, e) in two ways—by firsteliminating the parameter and then without eliminating the parameter.
14. Finddydxandd2ydx2for the curvex=t2+1, y=et-1. For which values oftis the curve concaveup?
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18. Find the points on the curvex=t3-3t,y=t2-3 where the tangent is horizontal or vertical.

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