A cycloid has parametric equations z =t - sint, y = 1 - cost, 0

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (2, 0,…

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Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

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

A: Consider the given parametric equations, xt=tyt=e-4tzt=5t-t5 Here we need to find the parametric…

Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

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

A: A detailed solution is given below.

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan L, , (3,…

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Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: The equation of the tangent line to the parametric equations, x =t +sint, y 4t-cost att 0 is y = -1…

A: As we know that; The slope of the tangent line to the given curve is equal to the first derivative…

Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Find the equation of the tangent line to the parametric curve at (1, 3). z =1+ Int y = t +2

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Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: Find the parametric equation for the line tangent to the r(t)=sinti+(t2-cost)j+etk curve t=0 at the…

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Q: Find parametric equations for the tangent line to the curve a-tcost, y-t, z- tsint at the

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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

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Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan Y. (4, 0,…

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Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

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 arc length of the curve with parametric equations x = e-t cost and y = e-t sint on the…

A: We have to find the arc length.

Q: Find the equation of the tangent line to right branch of the hyperbola π π x = sect, y = tant, ≤t≤at…

A: Given :x=secty=tant

Q: compute using the parametric equations I= cost, y = sin t, te (-x, 0) Write as a function (i) of t.…

A: Using chain rule,

Q: Find an equation of the tangent(s) to the curve with parametric equations x = t cost, y = tsin t…

A: Given- x=tcost , y=tsint To find - To find the equation of tangent to the curve with given…

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: A curve C has parametric equations X = tチ+1. dy (i) Find in terms oft. dx (ii) Show that there are…

A: We first find dy/dx

Q: Find equations for the a) tangent line and b) normal plane to the curve 1 x=t- cost, y = 3+ sin 2t,…

A: x=t-cost, y=3+sin2t, z=1+cos3t We know that rt=xt, yt, zt dxdt=1+sint, dydt=2cos2t, dzdt=-3sin3t At…

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: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

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Q: Find the slope of the tangent line to polar curve V3 T r = 4 – 6 sin 0 at the point 4 – 6 Preview

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Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

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Q: Find parametric equations for the semicircle x2 + y2 = a2, y > 0, using as parameter the slope t…

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Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

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Q: Find the slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

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Q: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan y/x ,…

A: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan(y/x).…

Q: Sketch the curve by using the parametric equation to plot points. Then, eliminate the parameter 0,…

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Q: x = 1+ vt, y = et X =1+1 Y. %3D

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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: Find an equation of the tangent plane to the surface at the given point. g(x, y) = arctan 2, (1, 0,…

A: This question is based on finding equation of tangent plane of function having two variables at a…

Q: Find parametric equations for the semicircle x2 + y2 = a2, y> 0, using as parameter the slope t =…

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Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

Q: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: r(t) = (e-t cos t, e-t sin t, e-t)

A: Given  rt=e-tcost,e-tsint,e-t First find derivative of given point dxdt=-e-tcost-e-tsint…

Q: x = V1 - i , y = t³ – 3t

A: We have to find derivative

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: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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