For the curve defined by r(t) = 3 cos (t)i + 3 sin(t)j + 5tk evaluate t S= | = ||*|| 7" ( )|| du to find the arc length function. 8 = Solve the arc length function for t: t = Parametrize (t) by arc length by substituting in the solved arc length function. r(s) =

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: 17. Find : t = 11T 6 sin t = Csc t =

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

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Q: How do the paths r1(t) = (cost,sin t) and r2(t) = (sin t, cost)around the unit circle differ?

A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

Q: 8. Find the principal value of Arc tanh(1 + j2)

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Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

A: Given : r(t)=3cos(t), t-4, 3sin(t) is the position function of a particle. To find : If the particle…

Q: x = 2 sin-1 1, y = In (1 – r²) (0<1s!)

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Q: A curve is defined by y=(1/3)sin(2x+1). Evaluate the angle between the tangent to the curve at x=2,…

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Q: Find the equation of the tangent line of the curve y = sin r + cos a at the point A(, v2).

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Q: A curve is given with x cos(pi x y) = x + y + 1. Find the tangent line and the perpendicular line to…

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Q: For r=sin40, (i) sketch the curve. (ii) Find the area of one loop of the curve.

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Q: 04) Find dy /dx for the following functions: a) y².cotx= [sin(x.y)]-¹ b) y = (lnx + x)tan

A: See the answer below

Q: L. Let h (x) = f (x) g (x). Find a. h' (1), b. h' (3), and с. h' (4).

A: According to the given information,

Q: Find the length of the curve traced out by the path c(t) Answer= = (cos(3t), sin(3t), 6t) for 0 ≤ t…

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Q: Suppose θ(t) measures the minimum angle between a clock’s minute and hour hands in radians. Find,…

A: Given that:  θ (t) measures the minimum angle between a clock’s minute and hour hands in radians. An…

Q: Find the length of the arc y = In(cos x) between the points (0, 0) and (pi/3, -In2).

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Q: Find the domain of the vector function 7(t) = Domain: {t| <t< }

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Q: 50° S. 80° R 60° 100 7. 7.

A: The measure of the arc length is double than the angle formed by that arc to the circumference of…

Q: ) If y = cos2x + 2cosx for 0 < x < 2n. Find the points at which the tangent line is horizontal.

A: Given function is y=cos2x+2cosx for 0≤x≤2π. To find the points at which the tangent line is…

Q: GIVEN: I': c(t) = (cos²t, sin²t), t = [0, 7] L(T) is the length of I FIND: L(r)

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