Find the length of the path over the given interval. (6(0 – sin(0)), 6(1 - cos(0)),

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A:

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A: xt, yt=sin3t, cos3t,   0≤t≤π Here, xt=sin3t,  yt=cos3t Now differentiating with respect to t, we get…

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A: Solve the following

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Q: Find the length of the curve. cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< n/4

A: We have to find the length of curve.

Q: Find the length of the path for c(t) = (4(0 – sin(0)), 4(1 – cos(8))) over the interval 0 < 0 < 2r.…

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Q: The approximation of 1 = cos (x² + 3) dx using simple Simpson's rule is: -1.57923 -0.93669 This…

A: The given integral is I=∫01cosx2+3dx To approximate the integral using Simpson's rule.

Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: Given the integral csc²u=cot²u+1 1+ cos2u 2 1-cos2u 2 sec²u=1+tan²u B cos²u=- sec (x-1) tan4…

A: According to our guidelines we can answer only one question or three subparts of a question. Other…

Q: A-Show that S 1, L{cos at} s2+a²

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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Q: Find the length of the curve over the given interval. r = 6 – 6 sin(0) on the interval 0 < 0 s 2n

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Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: If u(t) = (sin(4t), cos(2t), t) and v(t) = (t, cos(2t), sin(4t)), use Formula 4 of this theorem to…

A: Find u(t) . v(t) first then differentiate with respect to “t”.

Q: Calculate the length of the path over the given interval. (sin 4t, cos 4t), 0 <t <T

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Q: A periodic signal is given by r(t) = 3 cos(t) + cos (5t 2n - 2 sin (8t + 3

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Q: and as Use the chain rule to find sin(6) r = st, 0 = s + t3 dz as

A:

Q: Find the length of the path over the given interval. (2 cost − cos 2t, 2 sin t − sin 2t), 0 ≤ t ≤…

A: x(t)=2 cost − cos 2t y(t)= 2 sin t − sin 2t interval- 0 ≤ t ≤ π/2

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Q: Find / sin(2r) PV -dr R I +4 by invoking Jordan's lemma.

A: Sol

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Q: 8. Find the length of the given curve over the indicated interval. r(t)= (r', 3 cos(t), 3t) [] 0, 2

A: Given r¯(t)=t2,3cost,3t in the interval [0,π2]

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Q: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y²…

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Q: Compute the following. S3x?cos(x³)dx

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Q: Find the highest point on the cardioid r = 1+ cos 0.

A: We cal solve the problem by doing the derivative and set it to zero for finding theta.

Q: Show that r = cos20 is symmetric about the y-axis.

A: I am going to solve the given problem by using some simple calculus to get the required result.

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Q: The integral / 2' )cos(2*) dx takes the form k cosu du when u=2* and f (x) =x- 5. What is the value…

A: we use the formula ddx(ax)=ax lna

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Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: A particle moves in the xy-plane so that its position at any time t is given by x= cos(5t) and y =…

A: According to the questionx=cos5ty=t3

Q: Find the length of the curve over the given interval. =8 r = 7(1+ cos 0), 0 <0< 2n

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Q: Show that r = cos(2pi) is symmetric about the y-axis.

A: The solution of the problem is given in the next step.

Q: Find the value of k if 1 х cos(3x) dx 1 3* x sin(3x) + — сos (3x) + C. k

A: .1. ʃ (u.v)dx= u ʃv.dx - ʃ(d/dx(u) . ʃv.dx)dx       Where u and v are function of x 2. ʃ sin(ax) dx=…

Q: 19. For all positive angles less than 360°, if csc(2x +30°) = cos(3y- 15°), the %3D sum of x and y…

A: Given that csc(2x+30°)=cos(3y-15°) It is known that csc(x)=1sinx. So, 1=sin(2x+30°)cos(3y-15°)…

Q: Calculate the length of the path over the given interval. (sin 3t, cos 3t), 0 <t<+

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Q: Use an appropriate local linear approximation to estimate the value of cos(59°). cos(59°) ~

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Q: 4 sin 2t + 2 tan 2t = 0 %3D

A: 4sin2t+2tan2t=0

Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: The solution of the following Bernoulli's equation xy' + 2y = x¹(cos x) y² is

A: The correct answer is not given in options.The solution with the correct answer is given as

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Q: 16. So the maximum occurs at an angle of 0, but only if the angle is small enough. Explain why that…

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Q: 1) Find the fundamental period of the functionu +v, if any, by examining whether the functions u (t)…

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Q: Q1\ Prove the left side equal to right side in the following : * L-1 (s² + a²y² - [sin at + at cos…

A: We need to show that:L-1s2s2+a22=12asinat+at cos atWe will use convolution theorem to show the…