1. [0/1 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 10.3.006. Find dy/dx. x = Vt y = 2 -t dy = dx X Need Help? Read It Submit AnswerTutorial Exercise Find dy/dx and day/dx2, and find the slope and concavity (if possible) at the given value of the parameter. Parametric Equations Point x = 4 cos 0, y = 4 sin e 0 = - 4 Step 1 You know that the parametric form of the derivative is dyl de dy = de dx dx de Step 2 Consider the parametric equation y = 4 sin 0. Differentiating gives dy (4 sin 0) de de 4 cos ( 0) 4 cos (0) Step 3 Now consider the parametric equation x = 4 cos 0. Differentiating gives dx d -(4 cos e) de de -4 sin (0) -4 sin (0) Step 4 Simplify. dy 4 cos 0 dx -4 sin 0 cot ( 0) - cot (e) Step 5 Now, we can find the second derivative. day _ d( dy/ dx) dx 2 dx d - (-cot e) = de dx/ de -4 sin 0 X5. [0/2 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 10.3.031. Find all points (if any) of horizontal and vertical tangency to the portion of the curve shown. (Enter your answers as a comma-separated list.) x = cos 0 + 0 sin e y = sin 0 - 0 cos 0 -2nt S O S 2n horizontal tangents 0 = 0,It, - It, - 21t,2 n X vertical tangents 0 = 0, 2 2 ' 2 X 8 - _ 8 -6 .X 6 8 -8-7. [3/6 Points] DETAILS PREVIOUS ANSWERS LARCALCET7 10.3.038. Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm your results. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE.) X = cos 0, y = 2 sin 20 Horizontal tangents ( x, y ) = V2 2 2 ( x, y ) = V2 2 ( x, y ) = V2 2 - 2 X ( x, y ) = V2 2 - 2 Vertical tangents ( x, y ) = -1,0 ( x, y ) = 1,0 Need Help? Read It Watch It' 12. [012 Points] DETAILS PREVIOUS ANSWERS LARCALCEI'I 10.1063. Find the area of the surface generated by revolving the curve about each given axis. x=7t, y=4t, ostsg (a) xaxis