Find the slope of the tangent line to the given curve at the point corresponding to the specified value of the parameter. r=3+cos3θ          θ =π/2

Q: The slope of the tangent line to the graph of f(z) COS at a is Select one: O a. 00 2 Ob. 2

A: we hav eto find the slope of the tangent line of the given graph at a=π/2

Q: Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0S0< x.…

A: Given :           r=6 cosθ

Q: Find of the curve the curve lenght from t=o to t=2M given C: P(t) = (cos 3t) î + (sin 3t) Î + ? tVt…

A: Here I am attaching image so that you understand each and every step.

Q: At what points on the curve y=cot x is the tangent line parallel to the line y=-x ? Choose the…

A: Given that: y=cotx

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: For what value of t will the slope of a line tangent to x = 6 sin t, y = t² + t be 0?

A: We have to find t

Q: Find the expression for the tangent slope dy/dx for points on the Polar curve r= 6 +12 cosθ

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Q: Find the length of the curve over the given interval. r = 1 + sin θ, [0, 2π]

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Q: Find the length of the following curve: y = ln(cos(x)) from x=0 to x=pi/4

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Q: Find the length of the curve r = 4 cos 0

A: Given curve is r=4cosθ We have to find the length of the given curve. The length of the curve in…

Q: 13. Eliminate the parameter t, sketch the curve, and indicate the orientation. x=5 sint, y= 5cost,

A: We will square the both equations and then we will add them to eliminate the t

Q: Find the equation of the tangent line to the curve y = 6 sin a at the point (, 3). The equation of…

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Q: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: Determine the slope of the tangent line, then find the equation of the tangent line at the given…

A: For t=1,x=1+11=1+1=2y=1-11=0

Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

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Q: Suppose the position function of a particle is given by r(t)=(√3 sin(t), t-2, √3 cos(t)). If the…

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Q: Calculate the slope of the curve f(t) = 11 sin? (t) at the point where t = 3 radians. Slope : Round…

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Q: Which of the following is the tangent equation drawn to the pi/4 point on it? y = 25 - tanx curve…

A: This question is based on straight line. The general equation of a straight line is            y =…

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

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Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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Q: Find the equation of the tangent and normal to the following corce at the points indicated against…

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Q: An equation of the kangent and hormat. X+sinx líne to khe curve Y =xê

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Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: Graph the curve described by the function, indicating the positive orientation. r(t) = (2 cos t)i +…

A: The given function is- r(t) = (2cos t)i + 3j + (2sin t)k, for 0 ≤ t ≤ 2π

Q: Find the quadrant in which the point P(t) lies if the following conditions are true. (a) cost > 0…

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Q: Given the graph of r sin 2y = y cos 2x pictured at right, what is the point-slope equation for the…

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: Determine the slope of the tangent line, then find the equation of the tangent line at t = 4 8…

A: Given equation of curve is: x=8sint;y=cost Differentiating with respect to t we get,…

Q: Given x= cos0 y = cos 30 (a) find the points on the curve where the tangent is horizontal or…

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Q: Find the unit tangent of the following curve at the specified point. r(t) = 2ti + 1 · sin(2t)j+3 ·…

A: We have to find the unit tangent vector at t=pi/3

Q: Find the equation of the tangent line to the curve y = 8 sin z at the point The equation of this…

A: We know that the expression for slope of tangent to the curve at a point P(x, y) is: m=dydxp(x,y)…

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: Find all points on the curve y = cot x, 0 &lt; x &lt; p, where the tangent line is parallel to the…

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Q: Determine the slope of the tangent line, then find the equation of the tangent line at t I = 4…

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Q: Given the function f(x)=−2xcos(x), find f′(x). Then find the equation of the tangent line at at the…

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Q: t the given point, find the slope of the curve or the line that is tangent to the curve, as…

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Q: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

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Q: Please help

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Q: 1. a) Find the equation of the tangent line to the curve given by F(t) = (cos(nt), t, 1 + t2), for t…

A: First we find r(2) and r'(2). Then find equation of tangent line to given curve r(t).

Q: Find the length of the curve 7(t) = (ei cos(), ei sin(÷), e) n(4),e¿): for 0 <t < 5. CoS

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Q: For the following parametric equation, find the slope of the tangent line at the indicated point.…

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Q: Use the formula below to find the length of the curve defined by the equation x= cos^2 t , y = sin^2…

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Q: Determine the slope of the tangent line, then find the equation of the tangent line at t=pi/6.…

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Q: Find, correct to two decimal places, the coordinates of the point on the curve y =sin x that is…

A: Given that y=sinx So coordinate point is x, sinx.

Q: Find an interval of t-values with t > 0 such that c(t) = (cos t, sin t) traces the upper half of the…

A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

Q: Find the length of the curve r(t) = (e* cos t, et sin t , et), – In 4 <t<0.

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Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

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Q: find an equation for (a) the tangent line to the curve at P and (b) the horizontal tangent line to…

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Q: Find the tangent of ZH. J 4 H. 3-/6 Write your answer as an integer or as a decimal rounded to the…

A: Given triangle HJI