APPlicationS 32. The length of one arch of the curve y = sin x is given by V1 + cos² x dx. L = Estimate L by Simpson's Rule with n = 8.

Q: a. 1 y" + 2y' + y = -e™* b. x²y" + xy' + 4y = sin(2 ln x),x > 0

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Q: VARIATION OF PARAMETERS 1. (D^2+1)y= sec tanx

A: We have to solve by variation of parameters.

Q: Solve using: a) Newton's method of approximation b) Secant Method Es = .00005 COS X = X

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Q: (c) For a differentiable function f(x, y) with x = rcos0 and y = r sin0; (i) Draw the Tree diagram.…

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Q: A damping force affects the vibration of a spring so that the displacement of the spring is given by…

A: Given y=e-3t(cos6t+2sin6t)

Q: A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Construct…

A: Given wave function is yx,t=Asin2π0.1x-12t              (i) Where A is the amplitude of the wave,…

Q: Find the area of the region that lies inside the circle r= 6 sin(0) and outside the cardioid r= 2 +…

A: the region given is the circle r=6sinθ and outside the cardioid r=2+2sinθ

Q: 4 sin x Let f(x) = 2 sin.x + 6 cos x Then f'(x) = The equation of the tangent line to y = f(x) at x…

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Q: 8. The surface of a water wave is described by y 5(1+cosx), for -nSxST, where y = 0 corresponds %3D…

A: Given that the surface of water wave is described by y=5(1+cosx)  for -π ≤ x ≤ π , where y=0…

Q: 03// By using Gaussian quadrature, calculate the value of the given integration. dx sin(x) Use two…

A: First, transform the limits of integration such that the lower limit is -1 and the upper limit is 1…

Q: 2+cost Use IVT to show that g(t) = [0.7]. takes on the value 2.5 in the interval 1+ sin t

A: By using IVT we have to show that g(t) takes on the value 2.5 in the given interval.

Q: A particle starts at rest on a smooth inclined plane. At the end of t seconds, the position of the…

A: Given that, A particle starts at rest on a smooth inclined plane. At the end of t seconds, the…

Q: Using the method of variation of parameters find the general solution of the DE y" +y' tan t, 0<t<T…

A: please see the next step for solution

Q: cos(x) 1- cos(x) by miscellaneous substitution, the substitutionz=tan () In solving the…

A: Here f(x) = cosx/(1-cosx)  we have to determine the value of f(z) for z= 0.65

Q: For 0sts a particle moves along the x-axis. The velocity of the function is given by 2 v(t) =…

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Q: t+0 tan3 2t t+0 sin 10t 10.1 letcariorg line horizontal? At what points on the curve y = sin x + cos…

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Q: ind the length of the arc in one period of the cycloid x= t-sint ,y= 1-cost. The value of t run from…

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Q: Consider a x²-curve with df = 15. Obtain the x²-value that has area 0.975 to its left. Click the…

A: The degrees of freedom is 15.

Q: 3. A particle starts at rest on a smooth inclined plane. At the end of t seconds, the position of…

A: Please refer the attached image for complete solution

Q: = T Cos (4), what is the total distance :0 to t = 4? A particle has velocity function v(t) traveled…

A: The objective of the question is determine the total distance from the given velocity function…

Q: your answer(s). Eliminate the parameter t. x = 4 sint - 4, y = 4 cost – 3

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Q: The single positive zero of the function f(x)=x tanh() –1models the wavenumber of the water wave at…

A: Here x represents the depth of water. fx=xtanhx2−1 If a function f(x) takes opposite signs at two…

Q: rms of Q. at the value of P is halved wher x+1)². When x = 4, y = 100. %3D rms of x. of y when x =…

A: Variation: a) y∞(x+1)2 y=k(x+1)2 Where k is variation constant.this is the relation between x and y.

Q: C: 1- Find for the function: X²+ Siny =X.y² 2- Find the mnd dy por the fur etion - for the fum…

A: 1) Given: x2+siny=xy2 On differentiating the given function on both sides with respect to x,…

Q: long the x-axis and the tip of the blue pencil is moving along the y-axis. Th of the tips of the red…

A: In given question, concept of area of triangle is applied. Area of Triangle In a two-dimensional…

Q: A particle starts at rest on a smooth inclined plane. At the end of t seconds the position of the…

A: The root of the function can be calculated using the secant method. The formula for the secant…

Q: (c) For a differentiable function f(x,y) with x=rcose and y = r sin0; (i) Draw the Tree diagram.…

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Q: Secant Solve the roots of the curves below by using the Secant method in the given intervals.…

A: Iteration formula of Secant method: The iteration formula of Secant method is, xn+1 = xn-1-f(xn-1)…

Q: LH.S.-R.H.S. HW/ Brove-that: (1) 1-tanhf x sech'x 12 11

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Q: 1 3. y 4. 9. dy at x=5 using Newton's divided difference formula. dx Find the value of

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Q: The tube cross-section shown has inner radius of 3 cm and outer radius 6 cm and within the tube…

A: This question is about application of derivative

Q: Find the maximum and minimum values of the function y = 4 cos(0) 7 sin(e) on the interval [0, 2x] by…

A: Compute the critical points as follows.

Q: 4 sin(3f(x))·f'(x) dx (c) Let fbe a differentiable function on the interval [a,b]. Compute/a . Note:…

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Q: Let c be the number such that the area under y = sin x over [0, x] is divided in half by the line y…

A: Consider the provided question, The area under the y = sinx is find as by integration,

Q: A mass hanging from a spring is set in motion and its ensuing velocity is given by v(t) = - 5n sin…

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Q: 2 sin x Let f(x) 4 sin x + 6 cos x Then f' (x) = The equation of the tangent line to y = f(x) at a =…

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Q: Q1: Find the following: a. Differentiate with respect to the parameter t x = sin?t, y cos²t b. Find…

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Q: The waves from the lake remove pebbles from the shore at a rate modeled by the function R given by…

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Q: (1) C) What is y'(x) for a function defined by the equation x sin(ay) = y+ e" as it passes through a…

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Q: for the functions below: a) if y-sinu, u-3x+n find dy/dx at point(0,1) b) Find for the function y =+…

A: we are given: y=sin u and u=3x+π ⇒y=sin (π+3x)=- sin 3x ⇒dydx=-3 cos 3xdydx(0,1)=-3 cos 3(0) =-3…

Q: Forward Euler's method with step h = 0.1, is applied to solve y' = = (-1+ aj)y(x) where j = v-1 and…

A: Given that the function y'=dydx=-1+ajyx                 1 where j=-1 and a is some positive real…

Q: Find an equation of the tangent line to the curve y = 4x sin (a) at the point (T /2,27). Express…

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Q: (a) The volume produced by revolving the area enclosed by the first arch of y = sin(x) and the…

A: Given :   Y= sin x Integral of the first curve is 0 to pi Rotate around y axis that is x=0 Use the…

Q: 1. Using Newton-Raphson method, find a root with the starting value, xo = 1 for the function y = e¬*…

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Q: Let Compute Ә მა g(s, t) = (sin(s) - t,e', s) and f(x, y, z) = e²+²y+z (fog) at (0,0).

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Q: Find the acute angle between the two

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Q: Q. 5 The object of mass 1 kg is dropped from a hovering helicopter. The velocity v satisfies the…

A: Consider the given equation. dvdt+sintv2,v0=0 The value of h is 0.2 and we have to calculate the…

Q: sinh x (2) I = S dx, evaluate I; V1+cosh x

A: We have to evaluate  I=∫sinh(x)1+cosh(x) dx Let us consider   1+cosh(x) = t    then  sinh(x)dx=dt…