x=e"Cost = e"S int

Q: Consider the curve defined by the parametric equations X = cos t, y = 3sec t on the interval…

A: To eliminate t and find cartesian equation.

Q: 4. Find equations of the tangent plane and the normal line to the surface yz = arctan(2x+z) at the…

A:

Q: Find the length of the curve. The cardioid r= 3(1- sin 0)

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Q: The parametric equations for the paths of two objects are given. At what rateis the distance between…

A: Given: The parametric equations for the paths of two objects are given. At what rateis the distance…

Q: Find the area of the surface obtained by rotating the curve of parametric equations x = 10 cos³ 10…

A:

Q: The parametric equations for the motion of a charged particle released from rest in electric and…

A: Given x and y values.... Let us find dy/dx to draw the graph....

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

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Q: Find the equation of tangent plane and normal lines of the surface: t the point (1,3, 2).

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Q: The angle between tangent and the radius vector of the curve r 5(1- sin@) at 0= is %3D

A:

Q: Tangent drawn from the point (4, –3,10) to the intersection curve of z = x² and z = 25 – y² surfaces…

A:

Q: Find the slope of the tangent line to polar curve 5 r = 5 cos 0 at the point Vē' 4 2, Preview

A:

Q: Find the slope of the tangent line to the polar curve r = sin(70) at 0=. Enter as an integer or…

A:

Q: Find the equation of the tangent plane to the surface 3 – 12y – sin(r*:) = 0 at the point (2, 1,0).…

A: To find gradient of the function.

Q: What is a di¡erentiable curve’s unit tangent vector? Give an example.

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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: Find the points (x, y) at which the polar curve r = 1+ sin(0), has a vertical and horizontal tangent…

A:

Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

A: Given Surface is xz + 2xy + yz = 10

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

A: The tangent line to a parametric curve given by c(t)=< x(t) , y(t) , z(t) > at some point…

Q: of the points where the parametric equation y = 2 cost 0≤t≤ 2π will have vertical tangent. Determine…

A: Given is the parametric equation x=5sin2t , y=2cost   0≤t≤2π We have to find the point where the…

Q: Find the equation of the tangent line to the parametric curve at the indicated point. Show all work.…

A: Equation of tangent line : y - y0 = m ( x - x0 ) m is the slope of tangent line .

Q: Find the total distance traveled by a particle along the curve given in parametric form x=sint -t…

A:

Q: Find parametric equations describing the circle of radius 6 centered at (2, 3), drawn…

A:

Q: Chebyshev's theorem is used when there is a bell shaped curve

A: Chebyshev's theorem is used when we want to find the the upper bound  of the probability. And they…

Q: Two parametric equations are given by: x = cos (1), y sin (t) u- sin(t) v - cos(t) In one figure,…

A: Any point in the cartesian coordinate system is defined as x,y. The parametric functions are defined…

Q: Find parametric equations for the arc of a circle of radius 7 from (0,0) to Q = (14,0). æ(t) y(t)…

A: Given that  Radius of circle is 7  P(0,0)to Q(14,0) To find the parametric equations of the circle

Q: . Find the slope of the line tangent to the parametric curve x = 2cost and y = 2- cos²t for 0<t<n at…

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Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

A:

Q: Find the slope of the tangent line to the polar curve r = cos(e) at e =. Enter as an integer or…

A:

Q: Regionenclused by the_curve (r=2 cos20)-

A: Given:     r=2cos2θ

Q: 3) Find the radius of curvature for the parametric curve et cost, y = et sin t.

A: To find the radius of curvature. The radius of curvature is the inverse of curvature.

Q: Find the points (z, y) at which the polar curve r = 1+ sin(0), – sos has a vertical and horizontal…

A: The polar curve is r=1+sinθ. Suppose that x=rcosθ and y=rsinθ. That is,…

Q: Find the points (x, y) at which the polar curve r = 1 + sin(0), – < 0 has a vertical and horizontal…

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

A: The derivative dydx defines the slope of the tangent drawn to the curve.

Q: 3. x = 3+ 4 sin t ;y == 3 cos t – 4

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Q: 9. Find equations of tangent plane and normal line of surface e -z+ xy 3at point(2,1,0). %3D

A: Given a surface fx,y,z=ez-z+xy=3. To determine the equation of the tangent plane of the surface at…

Q: the max and min directional derivative and their directions; (4) the parametric equation of the…

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Q: Find the points (x,y)at which the polar curve r=1+sin(θ), −π/4 ≤θ≤π/4  has a vertical and horizontal…

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Q: Plot the cissoidr 2 sin 0 tan 0 and show that its equation in rectangular coordinates is x3 y2 2 - x

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Q: Two parametric equations are given by: x = cos' (t), y sin (t) u = sin(t) v - cos(t) In one figure,…

A: We have to make plots of y versus x and v versus u.

Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

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

A:

Q: Find the length of the parametric curve. X =t+ sint -T<t<π | ly=t2 + cost Set up the integral, then…

A: HEre we have to find the arc length of the given parametric curve

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

A: Given  x=e-3tcos8ty=e-3tsin8tz=e-3t

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

A: The given curve is -rt=lnt4i∧+t-4t+θj∧+t Ln t4k∧ - 1     t=to=4differentiating 1wrt t , we get…

Q: Find the length of arc of the curve y = √sec²t - 1 dt from the point where x = -to the point where x…

A:

Q: Consider the curve parametrized by: x = sin t, y = sin2t a. Eliminate the parameter b. Sketch the…

A: x = Sin t  ,  y= Sin2 t(a) Pw  sint = x          y  = x2

Q: Select the curve generated by the parametric equations. Indicate with an arrow the direction in…

A: The objective is to sketch the curve generated by the parametric equation with the arrow as t…

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: The length of the path describe by the parametric equations, x=(1/3)t^3 and y=(1/2)t^2, where 0≤t≤1,…

A: