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: Evaluate L₂Lova (4-3²) dydx -√4-x² by using polar coordinates.

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Q: -aluate tan t sec? t dt

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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: 45. The rectangular equation x² + y² - 2x=0 written in polar form is r = 2 cos.

A: The rectangular equation is x2+y2-2x=0

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: Find polar coordinates (r,θ) where r < 0 and 0≤θ≤2π of(√3,−1)

A: Given point in the rectangular coordinates is 3,-1. To find the polar coordinates r,θ, where r&lt;0…

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: + i5: and B = 4

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

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

Q: Evaluate ¹ (x²+x²2²)dzdx by using polar coordinates.

A: We have to evaluate the given integral using the polar coordinates. First we have to identify the…

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: 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: Evaluate | exp(-2²)dx, using an iterated integral and polar coordinates.

A: Using Cartesian coordinates to polar coordinates.

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: Convert the Cartesian coordinate (2,-1) to polar coordinates, 0 ≤ 0 0 r = √5 Enter exact value. 0…

A: for the given Cartesian coordinate (2,-1) the Polar coordinates are  r=5theta=2π-tan-1(12)

Q: Perform the indicated operation. (303-j19) (j2-1)

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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…

Q: The horizontal distance or range (R) of an object thrown at an angle 0 from the horizontal is…

A: Solved Below

Q: nJI = (3x + 2)', MHLK = (15x – 36)', and mZHMK = (8 %3D %3D K D 138 O 140° O 204 O 151 1 2 3 4

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