Q1: Find the length of the cardioid r= 1 + cos 0 0 < 0

Q: 6. (d) Sketch the curve described by x = 2 sin t , y = 2 cos t (you can use your calculator). (e)…

A: To sketch the curve x=2sint,y=2cost

Q: (7) Find the lengths of the curve r =2/(1 - cos 0), a/2<0<n.

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Q: Find the horizontal and vertical asymptotes of the curve

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Q: (a) Find the equation of the tangent line to the curvey = 2 sec x – 4 cos x at the point (, 2) %3D

A: Note: -Since you have asked multiple questions, we will solve the first question for you. If you…

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: A bullet fired from a gun follows the trajectory x = at, y = bt – 16t2 (a, b > 0) Show that the…

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Q: the length of the curve r = V1+ cos 20 for – -sos.

A: In this question, the length of the curve is to be determined. Length of Curve The length of the…

Q: The curves F₁(t) = (-5t, tº, -4t²) and F₂(t) = (sin(-3t), sin(-t), t — π) intersect at the origin.…

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Q: Find the tangent plane to the equation 2 = 4y cos(3x-5y) at the point (5, 3, 12). 2 =

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Q: Q.2 Differentiate the function y = 2x - 3x + 4 2) y = xcosx 3) y (1 + x2)3 sinx 4) y = 5) y = tan x…

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Q: Find T, Ñ and B for the curve 7 (t) = (5 cos(4t), 5 sin(4t), 2t) at the point t = 0 Give your…

A: the given curve is  r→(t)=5cos(4t),5sin(4t),2twe have to find a) T→(t)=unit tangent vector at t=0b)…

Q: #15) Determine y' a.y=sin 2x b. y = x² sinx co y = sin(-x) Determine #16.> d.) y = cos x sin x e-> y…

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Q: Find the equation of the line tangent to the cardioid r = 1+ sin(0) at Ô0 =

A: Given that,, Here, differentiate w.r.t. ,we get, We know that, To find: equation of the line…

Q: x(t)=sin2((pi/2)-t)  y(t)=cos4((pi/2-t) 0≤t≤pi/2 determine the slope of the curve at t= pi/4…

A: xt=sin2π2-t,  yt=cos4π2-t,  0≤t≤π2 Differentiating with respect to t, we get dxdt=2sinπ2-t·ddtπ2-t…

Q: How do the slopes of the lines tangent to the graph of y = tan-1 x behave as x S ∞?

A: The slope of the line tangent to the graph of y=tan-1x  at a point is the derivative of the function…

Q: Find the slope of the tangent line to polar curve r = 8 – 7 sin 0 at the point (8 %3D 2' 6

A: Given the equation of polar curver=8−7sinθ       .......(1)(8−72,π6)

Q: Q1 Find all the points of intersections of the curves r = 1+cose and r=1+sin0 r-1+ (0) r=1+cm(0)

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Q: What is the slope of the line tangent to the curve x = 7et – sin 6t and y = 6e6t - cos 6t at the…

A: We have to solve given problem:

Q: (1 point) Check by differentiation that y = 3 cos 2t + 3 sin 2t is a solution to y" + 4y = 0 by…

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Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

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