1. Given the equation for simple harmonic motion y = 4 sin 67(t – 3) +5. Find: a. Maximum displacement b. Frequency c. Value of y at t = 3

Q: Find the lengths of the curves x = 8 cos t + 8t sin ty = 8 sin t - 8t cos t,0 ≤ t ≤π/2

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Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 a) dy Find y' xp dy dx b) Find an equation of…

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Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (,0*? Y = 0 A B…

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Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

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Q: Given y= sin3x, dy at a = 3 is approximately

A: The given function is y=sin3x. Differentiate the given function as follows. dydx=ddxsin3x=cos…

Q: 1) Find the equations of the lines that are tangent to Y = 0.5(sin 2t) at the origin the curve COs…

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Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: To find: The equation of tangent to the curve and also find d2ydx2. Given: The functions are x=cos…

Q: O Find the equation of the line tangent to the curve at the given value of the parameter. x cost+…

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Q: Let C be the graph of the equation In(3y – 2e") = sinh“(Tx) – tan(y – 1). | dy (a) Find dr (b) Find…

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Q: 3. Given the equation y = In(cos(x)): What is dx/dy? secx -seox -tanx -cotx None of the choices.

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

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: We have given parametric equation x=4sint, y=2cost  We have to find the tangent line of the given…

Q: From your plot, find the time, t, when current, I is maximum. Find the time and the phase…

A: We are given the alternating current I = 5 sin(120πt + 0.52). Here, the unit of I is mA and of t is…

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: Question 4 Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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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: Solve for y in equation y e" sin x + e cos x - y+ C.

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Q: Find T, Ñ and B for the curve 7 (t) = (5 cos(4t), 5 sin(4t), 2t) at the point t = 0 Give your…

A: the given curve is  r→(t)=5cos(4t),5sin(4t),2twe have to find a) T→(t)=unit tangent vector at t=0b)…

Q: C) Find the equation of tangent to the curve 4x +9yi = 36 at the point (3 cos 0, 2 sin 0).

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Q: The exact value of the slope of the tangent line to the graph of the curve r = 5 + 4 cos(0), at e =…

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Q: For the implicitly defined curve: cos(7y) 5y sin(x) dy (e.g., find y' ). dx a. Find a formula for dy…

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Q: Find the general solution to the following equation y" (0) + 3y'(8) + 2y(0) = sin 0 – cos 0

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Q: Q.18 A curve 'C'is defined as x= a cos³0, y = a sin°0 in [O, t/2]. What will be the point P on curve…

A: Explanation of the answer is as follows

Q: A particle moves in a straight line with acceleration ?(?) = sin ? + 3 cos ?, initial displacement…

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Q: Match the equation with its graph. r(t) = cos(at)i + sin(xt)j + t?k, -1 <t< 1 %3D y 4 y 2.

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

Q: 5. x = cos 2t, y = sin 2t, 0 <t< T

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Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

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Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Tangent line for a curve at a point is a line which just touches it and is "parallel" to the curve…

Q: (cos t)y" + (sin t)y' – ty = 0,

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Q: Question 6 af Given f = esec (#) -ya+y, find dy (#) sec² (=) ye NO -y+In (y)

A: Given :f=esecxy-yx+y

Q: Question 24 2ay" =17 when t=V2. y' If x= Arctant3, y=/1+16, find the value of a if A 2/2 - 2/2 В ©…

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Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: I and y are related by 16 ye8 xy = sin (5 z). (a) Find dy at the point (0, 0). (b) Find the equation…

A: since given that x and y are related to each other as 16ye8xy=sin(5x)

Q: A b. C find an equation of the tangent to the curve at the given point (T/6,1) 4 sin ² x y = + y =…

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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: Let y = tan(2a + 8). . Find the differential dy when a = 5 and da = 0.2 34.47 Preview Find the…

A: To find the following a). The differential (d y) when x = 5 and (d x) = 0.2. b). The differential (d…

Q: Given the velocity and initial position of a body moving along a coordinate line at time t, find the…

A: The velocity of a body at time t is given as: vt=9π2cos3π2t On integrating v(t) with respect to t we…

Q: Find T, Ñ and B for the curve 7(t) = (2 cos(4t), 2 sin(4t), 5t) at the point t = 0 Give your answers…

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

A: Space Curves and T, N, B vectors The unit tangent vector T, the unit normal vector N and the unit…

Q: 2. A curve C with equation y = sin2x 0 < x <5, has a stationary point, P. e3x dy (a) Find an…

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Q: 4. Find du for the equation 3y? – cosy = x° -

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Q: Given: = 0 – sin 0; y=1– cose Find: dz2

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Q: dt cos?(t) dr dx du du + ex- at cos²(t) :-7u, ex dr du -7u dr t(0) = 0, x(0) = a, u(0) = e et heR.

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Q: If the position of a moving object is s(t)=(sin t)² meters above zero at t

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Q: (x € [0,x] T: sinx + cos(2y) = 1, y e -. 4: 4.

A: Given, sin x+cos2y=1

Q: Question 16 Find dy/dx at the glven point without eliminating the parameter, r=0 + cose and y=l +…

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Q: Find the general solution to the following equations: dy 2+ tan y dx

A: The given is the differential equation which can be solved as shown in step 2.

Q: 1) I = ft e" dt 2) I = Se-2x sin 2x dx

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Q: B The equation of a curve is y = cotx - 8 cos x, 0<x< π, find the coordinates of the points on the…

A: If the equation of the curve is given y=f(x)  Then we find dy/dx and then equating to 0 we get the…