6. (d) Sketch the curve described by x = 2 sin t , y = 2 cos t (you can use your calculator). (e) Find the distance traveled along the curve as t varies over 0

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A: The slope of the tangent line to the curve  y = f(x) at the point x= k is f '(k)

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Q: 2. (a) Find the tangent line approximation to sin(x) near r 0. (b) Is the tangent line approximation…

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A: To find: The circumference of the given curves. Given information: Concept used: If a functions are…

Q: 3. Find the length of the curve y = In (cos x), 0 <x <

A: we have to find length of the curve

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Q: Зп 2. Find the exact length of curve y = ln (cosx), * < x < n. 4

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Q: Suppose you start at the point (0,0, 3) and move 10 units along the curve given by 7 (t) = (3…

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Q: Find T and N for the curve 7(t) = (3 cos(5t), 3 sin(5t), 2t) at the point t = 0 COS Give your…

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Q: The derivative of y = 3 cos (V1-x²) + (1-x²), can be written as sin ( V1-x² ) – ( 1–x²) }) 3x…

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Q: Find the lengths of the curves x = ln (sec t + tan t) - sin t , y = cos t, 0 … t … pi/3

A: x=lnsect+tant-sint,  y=cost,  0≤t≤π3 Differentiating with respect to t, we get ⇒dxdt=1sect+tantsect…

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . 4

A: Given that, y = ln(cosx) To find length of curve, we have formula Length of curve = ∫ab1 + [f'(x)]2…

Q: Find the lengths of the curves x = 8 cos t + 8t sin t, y = 8 sin t - 8t cos t, 0 … t … pi/2

A: The length of the curve of any given function by the formula L=∫t1t2dxdt2+dxdt2dt. Here t1 and t2…

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Q: Find the exact length of the curve. y = 6 + cosh(3x), 0s x 8 중이nh(3) sinh(3)

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Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

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Q: 3. Find tangent line to x = 2 cot 0 y = 2 sin? 0 at 0 = t/4

A: First  differentiate  and find slope use equation of tangent line

Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

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Q: Find for the following functions: (4) y = x sinh 2x --cosh 2x (2) y = tan³√/cot(7x); (3) y= sin Imvr

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Q: ind the length of arc of the curve 6xy = x⁴ + 3, from the point where x = 1 to the point where x =…

A: Here given equation as 6xy=x4+3ory=16x3+3x Differentiate with respect to x…

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A: Let's find arc length of given curve in first quadrant.

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

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Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

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A: Given Data The equation of a curve is r=1+sinθ The interval is 0≤θ≤2π   The expression for the…

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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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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

A: Given: x=8cost+8tsinty=8sint-8tcost0≤t≤π2

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A: 1). Given y=tanx+sinx-3. To find: dydx Solution: Power rule of differentiation states that:…

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Q: Find the cosine of the angle between the curves (cost, -sin(t)/5, sint) and (cos(nt/3), sin(nt/3),…

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Q: 10 cos 0 and y = 10 sin³ 0, find the total length of the curve swept out by the point If x = (x, y)…

A: We have to point length of curve swept out by the point:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A: on solving this we get