22. x=sin t, y=cos t, 26 = f(t), y = g(t), where the range of f is [1, 4] and the range of g is [2, 3]. What can you say about the curve? 23. Suppose a curve is given by the parametric equations yg(t) in (a)-(d) with the parametric curves labeled I-IV. Give reasons for your choices. 24. Match the graphs of the parametric equations x f(t) and (a) 2 xA 2 + 1 (b) II xA 2 y A 2+ yA 2 x AVA14 (c) III 2 oth, y 2 t 2 t x (d) IV XA y 2+ 2 I 2 t

Q: Find the exact value of 0.049768 x³y²z ds, where C is the curve with parametric equations x = e¯t…

A:

Q: 1. Consider the parametric curve given by x = e-t, y = 1 – e-2t. Eliminate the parameter, sketch the…

A: Sketch the graph of the given parametric curve and determine the limits on values of x and y.

Q: 1. Find the second derivative of the parametric equations_x = a cost and y = b sin t

A:

Q: 4. Sketch the graph of the curve y = Vx and the tangent line in the Cartesian Plane using a scale of…

A:

Q: 1. Find the equation of the tangent line (s) to the following set of parametric equations at the…

A:

Q: 18. The parametric equations of a curve are given by x= at", y= 2at, where a is a constant and t a…

A: To find the equation of tangent line

Q: 3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1…

A: Given that: xt=cost1−costyt=sint1−cost

Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…

A:

Q: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

A:

Q: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

A:

Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: Suppose that a parametric curve C is given by the equations x = f(t), y = g(t)for 0 ≤ t ≤ 1. Find…

A: The parametric curve C is given by the equations x=ft,  y=gt  for  0≤t≤1.

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A:

Q: A curve is defined by the parametric equations Find the length of the curve from t=1 to the closest…

A:

Q: :2 cos(t) y = 3 sin(t) T = Find the slope of the tangent line to the parametric curve at the point 4

A:

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

A:

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

A:

Q: curve has the following parametric equations with parameter t. x=2t-1/2t and y=2t+1/2t. Find dy/dx…

A:

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given To find parametric equations for the tangent line to the curve with the given parametric…

Q: 7. The curve at right is given by the parametric equations t2 z = v2t. x = In t, y = Find its length…

A: Given that, x=lnt,y=t22 and z=2t. That is, r→t=lnt,t22 ,2t. It is known that, the length of the…

Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

A: The vector equation of the tangent line of the parametric curve r→t at point P is expressed by…

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

A:

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

A:

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 10 cos(0) + 3 sin? (0) and…

A:

Q: 3. A curve has parametric equations r = sin(3t) and y = cos(t) where t takes all real %3D values. dy…

A:

Q: 2. (a) Recall that or a parametric curve x = = f(t), y = g(t), where f, g are continuously…

A: Given: Q1 (a), x=t3+t, y=13t+2,  t∈R x=ft, y=gtht=dydx=g'tf't d2ydx2=dzdx, where z=ht To find: Using…

Q: 9. Show that the curve with parametric equations x = sin t and y = sin(t + sin t) for 0st s 2n has…

A: Given that the curve with parametric equations are x=sint,y=sint+sint. First find the slope that is…

Q: Let C be the curve defined parametrically by x (t) = cos (t), y (t) = sin (t) and z (t) = 3t, where…

A: The given integral:∫CF.drWhere Fx,y,z=x2+y2,2yx,z227And the curve C is given by:xt=cos t ; yt=sin t;…

Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

A:

Q: 00 1. 2. 3. Match the equations of the parametric curve to the graph. x = 3 sin t у %3D 2 сos t 1. x…

A: Here the equations form of ellipse.

Q: For problems 4 – 7 find the equation of the tangent line(s) to the given set of parametric equations…

A:

Q: 1. Find an equation of the tangent plane to the surface of z = sin(x – 2y) at the point (7.5.0).

A: First partially differentiate the function with respect to x,y and z and then proceed as shown…

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

A:

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

A:

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x? +² =…

A: Here finds the parametric equation for the tangent line to the curve of intersection.   where the…

Q: A curve has parametric equations x = 2 sin t ,y = cos (2t) + 2 sin t for −π/2≤ t ≤−π/2 . Find out…

A: Given : parametric equations x = 2 sin t , y = cos (2t) + 2 sin t for −π/2 ≤ t ≤ π/2     Note :…

Q: 8. The tangent line to the curve r(t) = Li+ej=t'k 2-t at the point P(1,1, -1) intersects the line…

A:

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Consider, r(t)=lnt4i+t-4t+8j+t lnt4kWe first evaluate r(t) at t=t0=4r(4)=ln44i+4-44+8j+4 ln44k…

Q: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

A:

Q: a) A curve is given by the parametric equations 1 where 1 <t<3. t' I = 2 lnt and y = - i. If L is…

A: We need to find length of curve.

Q: x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

A: Given Data: x=3lnt ......1y=4t1/2  ......2z=t3      ......3 x0, y0, z0=0, 4, 1   For the specified…

Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem

Q: 13. Consider the curve C given by the parametric equations x=2–3cos t and y = 3+2 sin t, for –sis 2…

A: Formula a) dy/dx b) y-y1 = (dy/dx)(x-x1)