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12. For this question consider the parametric equation x = 2t +1, y = - 4...
Question 11 Find the length of the curve with parametric equations x = 2t, y = 3t, where 0 <t < 1. 10 42-2 O 4V2 - 1 22-1 4/ Question 12 True or false: y=x cos x is a solution of the differential equation y + y = -2 sin x True False
you can skip question 1 Sketch the graph of x(t) sin(2t), y(t) = (t + sin(2t)) and find the coordinates of the points on the graph where the tangent is horizontal or vertical (please specify), then compute the second derivative and discuss the concavity of the graph. 1. Show that the surface area generated by rotating, about the polar axis, the graph of the curve 2. f(0),0 s asesbsnis S = 2nf(0)sin(0) J(50)) + (r°(®)*)de Find an equation, in both...
QUESTION 6 Define a set of parametric equations as X=2-2t and y=12-4 on the interval -2 ts2, where t represents time. a. The graph with respect to time is b. The direction of the graph with respect to time is c. The y-intercept is (0, d. The smaller x-intercept is e. The larger x-intercept is ( ,0).
This question gives you a pair of parametric equations. Find a rectangular equation for the plane curve defined by the parametric equations. =t+4, y=t, fort in (-0, 0) 9
Consider the parametric equations below. x = 2 + 4t y = 1-t2 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.(b) Eliminate the parameter to find a Cartesian equation of the curve. y = _______ Consider the parametric equations below. x = 3t - 5 y = 2t + 4 (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the...
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t) − cos(4t), where t denotes an angle between 0 and 2π. (a) Sketch a graph of this parametric curve. (b) Write an integral representing the arc length of this curve. (c) Using Riemann sums and n = 8, estimate the arc length of this curve. (d) Write an expression for the exact area of the region enclosed by this curve.
Question 8 (10 points) Consider the following parametric curve: æ(t) = ť- 2t+2, y(t) = ť- 2+ + 2t - 3 In the FIRST answer box, write the SLOPE of the tangent line at t-2 and in the SECOND answer box, write the EQUATION of the tangent line at t-2. You do NOT need to show work. -
Question 8 (10 points) Consider the following parametric curve: æ(t) = ť- 2t+2, y(t) = ť- 2+ + 2t - 3 In the FIRST answer box, write the SLOPE of the tangent line at t-2 and in the SECOND answer box, write the EQUATION of the tangent line at t-2. You do NOT need to show work. -
Question 6 14 pts Consider the curve C defined by the parametric equations: x f(t) y= g(t) = sint -t costt (d) Which picture shows the curve C? Recall the curve C is defined by : x= f(t) cos t g(t) = sint - t y 20 20 10 10F 0 -10 -10 -20 -20 -20 10 -20 10 C 20 -10 0 10 (i) (ii) X 20 20 10 10 0 0 10 -10 -20 -20h -20 10 -20...
"A Watch t use 0.62/1.25 points 1 Prefous Anewe LaPCalc 10 B.018 Consider the follewing. x-3 cos 0 y5 sin 8 (a) Sketch the curve represented by the parametric equations (indicate the orlentation of the curve) y 10 -2 21 2 -10 21 -10 (b) Eliminate the parameter and write the corresponding rectangular equation whose graph represents the curve Adjust the domain of the resuting rectangular eqvation if necessary oed Heln? 0/1.25 points | Previous Answers LarPCalc8 10.6.042 6. Find...