Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for...
What are the critical points for the plane curve defined by the equations (t) = tant, y(t) = cost, and <t< ? Write your answer as a list of values of t, separated by commas. For example, if you foundt = 1 ort = 2, you would enter 1, 2.
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
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
Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve ★17)x-t3 + 1.y=t3-1,for t in [-2, 2] 17) Give two parametric representations for the equation of the parabola. 18) 18) y=x2 + 6x + 15 Find the partial fraction decomposition for the rational expression. Use a table of values to graph the plane curve defined by the following parametric equations. Find a rectangular equation for the curve...
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...
Question 15 < > Find the length of the curve for the following parametric equations for 2 <t < 10. Find its exact value, no decimals. r(t) = e' - 36 ly(t) = 2461/2 Length =
3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=etcost, yr etsint, z=et; (1,0,1) (b): Find the unit tangent vector T, the principal unit normal N, and the curvature k for the space curve, r(t) =< 3 sint, 3 cost, 4t >.
Question 20 0.1 p1 Find a rectangular equation for the plane curve defined by the parametric equations. x = 5 cost, y = -2 sint; Osts 21 4x2 + 25y2 = 100;-5 sxs 5 O 4x2 - 25y2 = 1;xzı 4x2 - 25y2 = 100; x 25 O 4x2 + 25y2 = 1;-} sxs O None Question 21 0.1 pts Solve.
Question 19 Q19 V3. Find the x-y equation defined by the parametric equations of the curve x=t+6 ly=41-t². y=5+12x– x2 y=5–12x– x2 • y = 5-x² y=77-8²
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...