Solve the Goursat problem: [Utt Utt- c²Uxx u|x-ct=0 = x² u|x+ct=0 = x¹. nt: Use the formula for general solutions of wave equation on the real line. = 0 =

Q: -aluate tan t sec? t dt

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Q: Find the equation of the curve whose parametric equations are x = 1 + 4 cos 0, y = 2 + 3 sin 0, 0 €…

A: The given problem is to find the equation of curve whose parametric equations…

Q: QUESTION 1 x(t) = t – t2 y(t) = t3 Find dy/dx whent = 2. Round off to two decimal places.

A: Given: xt=t-t2, yt=t3 we know that dydx for given function is given by dydx=dydtdxdt=ddtt3ddtt-t2…

Q: Q3// B Verify that dv3p'sin Ddpd@d owhen using spherical coordinate

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Q: Q.1/Consider the following parametric functions y =1-cost and x =t -sint Find the following : dy a-…

A: We differentiate the function here.

Q: Solve the wave equation using Fourier Transform: o'u ou - ∞ 0 %3D -12x utx, 0) = H(x)e u, (x, 0) =…

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Q: Determine the angular frequency of the sinusoid (a²b² a x =- cos ab

A: Given: x=abcos(a2b2tπ-abπ)

Q: Write the parametric equations x = = 5 sin² 0, y = 3 cos² 0 e given Cartesian form. 3sqrt(1-x^2/25)…

A: Given query is to find the Cartesian equation.

Q: a) Find the directional derivative of S = In(2x +3y) at point (-1,1) in the direction ef 4i - 3i

A: The directional derivative of a function f(x, y) in the direction of the unit vector (a, b) is given…

Q: 2 Express the flowing equation in Cartesian equationr = 1-cos e

A: The given polar equation is: r=21-cosθ

Q: Eliminate the parameter in the parametric equations x = 7+ sint, y = 2+ sint, for 0sts, and describe…

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Q: The equation of the tangent line to the parametric equations, x = sine, y =20+ cose at e = 0 is y =

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Q: 1. x (0) = 0 + cos 0 y (0) = 1+ sin 0 given that

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Q: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

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Q: Determine an equation for the sinusoidal function shown. 2 2 2 -1 -2 O a) y--2cosx O b) y = -coS TX+…

A: We have to determine the sinusoidal function of the following graph -

Q: Write an equation of the tangent line to the parametric equation at the given value of t. Please…

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Q: Integral of Vector A= 2p sin(@)ap +0.5z2cos(9)az along L1 4Y L2 L1 180° L3 30° -5 0. 12.5 20 -12.5

A: integral of vector a = line integral (A.dl) from given figure  we will A.dl then we will calculate…

Q: Eliminate the parameter t from the parametric equationsx =3 +sin t and y = cos t - 2.

A: Given: x=3+sint and y=cost-2 We have to eliminate the parameter t from the parametric equations.…

Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

Q: Find the coordinates of L" if ALMN with L(1, 2), M(-2, 6), and N(-1, 5) is rotated 90° about the…

A: Given: L(1,2) , M(-2,6), and N(-1,5)

Q: x=t3/3  y=t2/2     0<t<1  resolve the parametric equation

A: Given that , x=t3/3  y=t2/2     0&lt;t&lt;1  Resolve the given parametric equation.

Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: EXERCISE 2.2 An automobile follows a circular road whose radius is 50 m. Let x and y respectively…

A: Given, v = 0.5 . s - 0.0025 . s2  r = 50m a = 0.6 g From kinematics acceleration can be defined by…