1. Consider the curve parameterized by x(t)=4(t^21), y(t)=2e^2t , tR . Determine an equation of the formy=f(x) for the tangent line to the curve whent=1. y=
2. Convert the point(9,11/3 ) from polar coordinates to Cartesian coordinates. Give exact values for x and y.
3. Convert the point (4 3,0) from Cartesian coordinates to polar coordinates for0<2. Give exact values of r and (Remember to typesqrt(x)forx andpifor.)
4. Consider the curve defined in polar coordinates by r()=4cos(5), [0,2] Determine the slope of the tangent to this curve when=/4.
5. Determine theexactarc length of the curve defined parametrically by x(t)=(1/2)t^216t, y(t)=(16/3)t^(3/2)+9, 0t2. L=