The wave equation of physics is the partial differential equation o'y d²y at² əx² Where c is a constant. Show that if f is any twice differentiable function then

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Q: = ln(x² + y²). Show that b.Let z = 8²z əx² dy² 0² + = = 0

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A: Given , In a triangle ABC

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Q: elow is the graph of a function f(x) -5 -4 -3 -2 What is the value of the limit -5 -3- -2- -1- 0 -14…

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Q: Verify the following identity: sin(a + 3) + sin(a− B) = 2sinacos

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Q: Evaluate the following integral in cylindrical coordinates. 6 √2 √√4-x² SS S 0 0 X 2-y2 dy dx dz 6…

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Q: π 4 18. (sin x − 1)dx + √ (cos x + 1)dx 0 0 f -4 4

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Q: 3. Find an equation for the tangent line at the given point. x+x²) ¹⁰, y = (1 + x + (0, 1)

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Q: calculate d2y/dx2 when y=-3x2+4x

A: The given function is .We have to find the value of .Use the derivative formulas,

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Q: 59. On what interval is the curve 1² o ²² + 1 + 2 dr y = S₁² ₁ concave downward?

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Q: 7. Consider a balloon having a spherical shape with volume given by V = (4/3) Tr³. Suppose the…

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Q: Show that the function f(x) = x + 5x + 1 has exactly one zero in the interval [-1, 0]. Which theorem…

A: Given functiin is f(x) =x4+5x+1.Now to check there is any zero in the interval [-1, 0] we use…

Q: Find u (v x W). u = (3,3,3) (5,9, 0) V = w = (0, 0, 3)

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Q: Find the determinant -12 3 21 of the matrix. 0 3 9 -6 -3 6

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Evaluate the following integral in cylindrical coordinates. 8 √64-x²√x² + y² s s S S S (x² + y²-1/²…

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Q: A BALLOON IS RISING AT A CONSTANT SPEED OF 8ft/sec.. A BOY IS CYCLING ALONG A STRAIGHT ROAD AT A…

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Q: Question 3. Find F where and F(√) = 3. F'(x) = 2x cos(x²)+7√√π

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Q: Solve the following equation on the interval [0, 2]: -sin2xcos2x = -5cos2x No solution 0,30 0,0 O, ,…

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Q: Consider the following vector field. F(x, y, z) = 3xye²i+yzexk (a) Find the curl of the vector…

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Q: Find the eigenvalues of the symmetric matrix. (Enter your answers as a comma-separated list. Enter…

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Q: Determine which set of vectors is not orthogonal. n tonight F1 ! O V = 5i; w = 2i v=8i +4j; w=i-2j…

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Q: Find the area of the parallelogram with vertices  P(2, 1, 3), Q(3, 4, 4), R(8, 9, 11), and S(7, 6,…

A: Vertices of the parallelogram are P(2, 1, 3)Q(3, 4, 4)R(8, 9, 11) and S(7, 6, 10)