6/26/2017 10.3 Mi Almaamariya
Math 1960, section 501, Summer 1 2017
Instructor: Mahboub Baccouch WebAssign
10.3 (Homework)
Current Score : – / 100 Due : Monday, June 26 2017 11:59 PM CDT 1. –/10 pointsLarCalcET6 10.3.001. Find dy/dx.
x = t2, y = 5 − 2t dy =
dx 2. –/10 pointsLarCalcET6 10.3.005. Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the
parameter. (If an answer does not exist, enter DNE.)
Parametric Equations Point
x = 9t, y = 6t − 5
dy
dx t = 2 = d2y
dx2 = slope concavity: ­­­Select­­­ http://www.webassign.net/web/Student/Assignment­Responses/last?dep=16151180 1/6 6/26/2017 10.3 3. –/10 pointsLarCalcET6 10.3.009.MI.SA. This question has several parts that must be completed sequentially. If you skip a part of the question,
you will not receive any points for the skipped part, and you will not be able to come back to the
skipped part. Tutorial Exercise
Find dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given value of the
parameter.
Parametric Equations
x = 4 cos θ, y = 4 sin θ Point θ = π 4 4. –/10 pointsLarCalcET6 10.3.017. Find an equation of the tangent line at each given point on the curve.
x = t2 − 4, y = t2 − 2t at (0, 0) at (−3, −1) at (−3, 3) http://www.webassign.net/web/Student/Assignment­Responses/last?dep=16151180 2/6 6/26/2017 10.3 5. –/10 pointsLarCalcET6 10.3.026. Find the equations of the tangent lines at the point where the curve crosses itself.
x = t3 − 6t
y = t2
y = (negative slope)
y = (positive slope) http://www.webassign.net/web/Student/Assignment­Responses/last?dep=16151180 3/6 6/26/2017 10.3 6. –/10 pointsLarCalcET6 10.3.029. Find all points (if any) of horizontal and vertical tangency to the curve. Use a graphing utility to confirm
your results. (If an answer does not exist, enter DNE.)
x = 5 − t, y = t2
Horizontal tangent
(x, y) = Vertical tangent
(x, y) = 7. –/10 pointsLarCalcET6 10.3.043. Determine the open t­intervals on which the curve is concave downward or concave upward. (Enter your
answer using interval notation.)
x = sin t, y = cos t, 0 < t < π Concave upward Concave downward http://www.webassign.net/web/Student/Assignment­Responses/last?dep=16151180 4/6 6/26/2017 10.3 8. –/10 pointsLarCalcET6 10.3.047. Find the arc length of the curve on the given interval. (Round your answer to two decimal places.)
Parametric Equations Interval π
x = e−t cos t, y = e−t sin t 0 ≤ t ≤ 2 9. –/10 pointsLarCalcET6 10.3.065. Find the area of the surface generated by revolving the curve about each given axis.
x = 3t, y = 3t, 0 ≤ t ≤ 5
(a) x­axis (b) y­axis http://www.webassign.net/web/Student/Assignment­Responses/last?dep=16151180 5/6 6/26/2017 10.3 10.–/10 pointsLarCalcET6 10.3.081. If y is a continuous function of x on the interval a ≤ x ≤ b, where x = f(t) and y = g(t), then
b a y dx = t2
t1 g(t)f '(t) dt where f(t1) = a, f(t2) = b, and both g and f ' are continuous on [t1, t2]. Use a computer algebra system and the result above to match the closed curve with its area.†
Ellipse: (0 ≤ t ≤ 2π) x = b cos t
y = a sin t 2
ab
5
5
Ï€a2 2
2πa2 πab
2Ï€ab
6πa2 http://www.webassign.net/web/Student/Assignment­Responses/last?dep=16151180 6/6

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