Find the points on the cardioid r = 4(1 – sin0) at which there is a horizontal tangent line, a vertical tangent line, or a singular point.

Q: At what points (r, 0) on this curve are the tangent lines horizontal? Use 0 < 0 < 2n. r = 1- sin 0

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Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: 5. Determine the equation of the tangent line to (a) r=2 sin 0 at 0 6 (b) r=1+cos 0 at : 2

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Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: ind the equation for the tangent lin to y- fcx) at the specified point. fcx) where x=1 x2

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Q: Find the equation of the tangent line to sin-(x - 2y) = 2xy – 1 %3D (1). at the point

A: Given,            The equation of the line is sin-1x-2y=2xy-1 and the point is 1,12.We know that,…

Q: find the tangent line of the curve (1– sin(1).tcos(1)) at the vale t(0) = T, (and so at the point(…

A: The curve is defined by the equations: x(t)=(t-sin(t))    and    y(t)=tcos(t)

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: Find the points on (t + sin t, t − 2 sin t) where the tangent is vertical or horizontal

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Q: find y'' for the curve cosx-siny=4

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Q: Find an equation for the tangent plane to z = cos(x2 + y2) at the point /等,0).

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Q: 5. Determine the equation of the tangent line to (a) r = 2 sin 0 at 0 = (b) r=1+ cos 0 at 0

A: We have to find equation of tangent line.

Q: Find the slope of the tangent line to the curve at the given value of the parameter. r=cose at 0= -…

A: Given         r = cos θ ---------------------------------------(1) Differentiating with respect to…

Q: Find an equation of the tangent line at the point specified.

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Q: 3 sin (t) cos“ (t)dt

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Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find the equation of the tangent line to the given function at z = a. w(2) = tan (3x) +x, a=0 3 !!

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Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: nd the points at which f(x) = cos² x has a horizontal tangent line. %3D

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Q: 5. Determine the equation of the tangent line to (a) r = 2 sin 0 at 0= (b) r=1+ cos 0 at 0=

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Q: 2. Find equation of the tangent line at the point P given by t = where x(t) = cos (t) %3D y(t) =…

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Q: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

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Q: Find the equations of the tangent lines x = 2 − π cos t, y = 2t − π sin t at the point where the…

A: Given :       x=2-πcost, y=2t-πsint

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

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Q: Find the equation of the tangent to the curve at t = 0

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Q: Find the arc length of the curve x = a cos3θ, y=a sin3θ in [0,2π].

A: The arc length formula for the parametric curve on the interval [a,b] is given by: Hence compute…

Q: Find the point on the cycloid c(t) = (t − sin t, 1 − cos t) where the tangent line has slope 1/2.

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Q: Prove that the segment of the normal to the curve x = 2a sint +a sint cos't, y = -a cos't contained…

A: First find derivative then equation of normal line ,and point of coordinate axes and then use…

Q: f(x,y) = 4x² + y² + 2 at the point wherex = 1 and y = 1.

A: The equation of the tangent at point (1,1) is: z=f(1,1)+fx(1,1)(x-1)+fy(1,1)(y-1)

Q: 8. Find a parameterization of the tangent line to r(t) = (cos(t), sin(2t)) at the point

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Q: Find the points on the given curve where the tangent line is horizontal or vertical, where:…

A: Consider  the given information: Let  r=1-sin(θ)  ,0⩽θ⩽2π To find the points where the tangent line…

Q: Prove that all normal to the curve x =acid+at sin t, Y=a sin t-atcost.Are at a distance a from the…

A: We need to prove that normal to the given curve are at a distance of a from origin.

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: Find the arc length of the graph of the function over the interval. y = In(sin z);

A: Given,          y=lnsinx ; π4,3π4

Q: Please solve

A: Parametrization of tangent lines is given by

Q: Find the point of intersection of the tangent line to v=sin(2r) at y=0 and the line %3D x+2y=5.

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Q: Find an equation of the tangent line at the point specified.

A: Consider the given equation as And

Q: Determine the equation of the tangent line to (a) r = 2 sinθ at θ =π/6 (b) r =1 + cosθ at θ =π/2

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Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

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Q: Determine the equation of the tangent line to the graph of g(x) = Sm, [1 – sin(ne')]dt at %3D In x…

A: We have to find the equation of the tangent line to the graph of gx=∫lnx01-sinπetdt at the point…

Q: Find the point at which the tangent line to the curve r= (1+sin e) is parallel to the х-ахis?

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Q: Find the points on the curve r = 1– sin 0 - where the tangent line is horizontal or vertical.

A: To find out the points on the given curve, where the tangent line is horizontal or vertical.

Q: Find the tangent plane to the equation 3y cos(5x – 4y) at the point (4,5,15)

A: z=3y cos5x-4y Let, Fx,y,z=3y cos5x-4y-z=0  ......(1) Now,  Fx=∂Fx,y,z∂x=-3y sin5x-4yx5-0…

Q: Find the slope of the tangent line for the curve r=sin⁡2θ at the point where θ=π/4.

A: Given,

Q: Sketch the cardioid r = 3 cos 0 and find the coordinates of the points on the cardioid where the…

A: Given polar equation is r=3cosθ

Q: Find the points on the given curve where the tangent line is horizontal. r = 2 cos 0

A: Follow step 2 .

Q: Find the equation of the tangent line to the curve r=cosθ at θ=π/4.

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

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