12. Given xcsc(v) – cot(v) = 1, what is y'? 1 A) х coty - cscy 1 B) x csc*y- secy 1 C) x tany – csc²y 2 1 D) x cscу — secy

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A: First, we find the point on the surface where the tangent plane would be drawn. Next, we calculate…

Q: c) A curve has a parametric equation x = 2t - 1 and y = t* -t'. dy Evaluate dx? 1 at t = 2

A: Given, The parametric equations x=2t3-1, y =t4-t3.

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Q: x =t +2 'y = t² - 1it E [-3,3] x = 4 cos t b) y = 3 sintit e [0,2m) graph graph a) Eliminate the…

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Q: Which of the following gives the length of the curve y x2 + 2x from x = 0 to x = 5 ? (x2 + 2x) dæ I…

A: Length of the given curve will be

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Q: 2. True or False: If the parametric curve x = a(t), y = b(t) satisfies d'(5) = 0 and b' (5) = 1 then…

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Q: Consider the curve C in R$ given by: r(t) = (e' + t, e' – t, 4e"/²) con 0<t<1 An expression that…

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Q: Find the derivative of y. 30) y = In (sinh 5x) D . sinh 5x A) coth 5x B) 5 csch 5x C) 5 coth 5x

A: We can answer the question as below.

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A: Given parametric curve, x = t+sin(t) y = t-cos(t)

Q: Find the length of the curve. The curve r= 8,/1+ sin(20), 0 <0< 4 A) 27 C) 8(7+ In(m

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Q: F(t) = %3D a. elliptical helix |F(t) = b. conical helix %3D ]F(t) = c. line d. circular helix…

A: We will use standard parametric form of these curve to match   For circle x = a cos(t) y = a sin(t)…

Q: iv is analytic = -11..

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Q: s"(1– 21) e) s= coS f) 4t y = t+1 2 x +x g) y= sin 3x h) y=e*

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Q: 9. Find the exact length of the parametric curve for the given interval. x = 4t 2 - 3, y = 3t, 0 St5…

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Q: 2п +1 E. Σ Зп +2 Е. n=0

A: The given data is: ∑n=0∞2n+13n+2  Solve using the integral test.

Q: 4) Evaluate (¹ + tany)dx + xsec²ydy where C is the curve Y=X²-1 from (1,0) to (2, 3)

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Q: fhy Find derivative uslng differentiatlon do not Slinplify deriratives axtb CXtさ rules 1if(x)=…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: The height of a chair on a Ferris wheel is given by h 5.7 sin (0. 21t – 1.58) +7.9 - where h is the…

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

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Q: A curve is defined by the parametric equations x-[*cos z dz, y- [sin z dz, tz 1. X= Find the length…

A: Consider the provided question, A curve is defined by the parametric equation x=∫8tcoszzdz,…

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