(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 10 0 10 10 (iv) X (e) Find an equation for the tangent line at the point t = r. Write your solution here 20 20 O X 20 O x
(f) Find an expression for the arc length of C' from t = -r to t = T, and approximate this using the upper Riemann sum for n = 4 Recall the curve C is defined by : x f(t) g(t) = sint - t costt y Write your solution here
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Question 6 14 pts Consider the curve C defined by the parametric equations: x f(t) y=...
(d) Which picture shows the curve C? Recall the curve C is defined by x f(t)...
(d) Which picture shows the curve C? Recall the curve C is defined by x f(t) cost t yg(t) sint - t 2아 2아 10 10 0 0 -10 -10 -2아 -20 20 10 20 -20 10 -20 -10 0 -10 (i) (ii) X X 2아 20 1아 1아 아 0 -10 -10 -20 -2아 10 20 -20 -10 10 20 -20 -10 0 0 (iv) (iii) X X (e) Find an equation for the tangent line at the point...
Let the curve C in the (x, y)-plane be given by the parametric equations x =...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
Consider the parametric curve given by x(t) = 16 sin3(t), y(t) = 13 cos(t) − 5 cos(2t) − 2 cos(3t...
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.
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et ...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
Solve C and D part please Sketch the curve represented by the parametric equations (indicate the...
Solve C and D part please
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.(Can you name the curve?) (a) r = sin 0, y = cos, - SOST (b) x = 4 sect and y = 3 tant 3 3 (c) r=-1+ z sint and y = cost for -A <t <3 (d) x = cosht and y cosh 3t (no need to sketch...
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with...
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t € (0,2) (a) Compute the length of the curve C. (b) Parametrize f(t) with respect to arc length measured from t=0. (c) Determine the curvature of C.
Question 11 Find the length of the curve with parametric equations x = 2t, y =...
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
Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for...
Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for the plane curve defined by the equations r(t)o(2)(t)1in(2t), and t<T? Write your answer as a list of values of t, separated by commas. For example, if you found t 1 ort would enter 1,2. 2, you Provide your answer below:
Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for the plane curve defined...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0)...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0) sin(8). Then, dy f() cos(0) + f (0) sin(e) d/ where / --f(8) sin(0) + / (8) cos(8) do Use this formula to find the equation in rectangular coordinates of the tangent line to r = 4 cos(30) at 0 = (Use symbolic notation and fractions where needed.)
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 +...
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
(d) Which picture shows the curve C? Recall the curve C is defined by x f(t) cost t yg(t) sint - t 2아 2아 10 10 0 0 -10 -10 -2아 -20 20 10 20 -20 10 -20 -10 0 -10 (i) (ii) X X 2아 20 1아 1아 아 0 -10 -10 -20 -2아 10 20 -20 -10 10 20 -20 -10 0 0 (iv) (iii) X X (e) Find an equation for the tangent line at the point...
Let the curve C in the (x, y)-plane be given by the parametric equations x = e + 2, y = e2-1, tER. (a) Show that the point (3,0) belongs to the curve C. To which value of the parameter t does the point (3,0) correspond? (b) Find an expression for dy (dy/dt) without eliminating the parameter t, i.e., using de = (da/dt) (c) Using your result from part (b), find the value of at the point (3,0). (d) From...
1. a. Consider the curve defined by the following parametric equations: r(t) = et-e-t, y(t) = et + e-t where t can be any number. Determine where the particle describing the curve is when tIn(3) In(2). 0, ln(2) and In(3). Split up the work among your group Onex, vou l'ave found i lose live polnia, try to n"惱; wbai ille wlu le curve "u"ht lex k like. b. Verify that every point on the curve from the previous problem solves...
Solve C and D part please
Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter.(Can you name the curve?) (a) r = sin 0, y = cos, - SOST (b) x = 4 sect and y = 3 tant 3 3 (c) r=-1+ z sint and y = cost for -A <t <3 (d) x = cosht and y cosh 3t (no need to sketch...
3. (12 points) Consider the curve C defined by r(t) = (4 sint, -4 cost,0) with t € (0,2) (a) Compute the length of the curve C. (b) Parametrize f(t) with respect to arc length measured from t=0. (c) Determine the curvature of C.
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
Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for the plane curve defined by the equations r(t)o(2)(t)1in(2t), and t<T? Write your answer as a list of values of t, separated by commas. For example, if you found t 1 ort would enter 1,2. 2, you Provide your answer below:
Find the Derivative of a Curve Defined by Trigonometric Parametric Equations Question What are the critical points for the plane curve defined...
A polar curve r = f() has parametric equations x = f(0) cos(8), y = f(0) sin(8). Then, dy f() cos(0) + f (0) sin(e) d/ where / --f(8) sin(0) + / (8) cos(8) do Use this formula to find the equation in rectangular coordinates of the tangent line to r = 4 cos(30) at 0 = (Use symbolic notation and fractions where needed.)
25. Given the following parametric curve X(t) = -1 + 3 cos(t) y(t) = 1 + 2 sin(t) 0<t<21 a) Express the curve with an equation that relates x and y. 7C b) Find the slope of the tangent line to the curve at the point t c) State the pair(s) (x,y) where the curve has a horizontal/vertical tangent line. 27.A particle is traveling along the path such that its position at any time t is given by r(t) =...
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