Let u(x,y,t)=(1/t)exp[-(x²+y²)/4t] where exp denotes e to a function. Show that u(x,y,t) satisfies the 2-dimensional heat equation ut-Uxx+Uyy. Hint: product rule...

Q: Sketch the graph of the parametric equations x = sint, y = 2 cos(3t), π ≤ t ≤ 27. Clearly label the…

A: We are to sketch the graph of the parametric equationsx = sint, y = 2 cos(3t), π < t < 2π.…

Q: g(x, Y, z) = /x² +z-2 + sin(xy – x²)

A: Let's find.

Q: Flux of F(x,y) = 5 x î +3 y ĵ across the circle x? + y? = 1 (anticlockwise) is - 8 T Can not find.

A: Use the Gauss’ Divergence theorem,: Use the Gauss’ Divergence theorem,

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Q: yyx² +y? F(x,y) = - is a homogeneous function of degree

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Q: z* = U(x, y) + iV(x, y), determine U and V. Verify that the C-R If f(z) = conditions are met at all…

A: First we have write given function I the form of U and V-

Q: Consider the IVP: 1 y"(t) + 2y'(t) + 2y(t) = 1², y(0) = y(0) = 0 (a) The complementary function yo…

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Q: Let f(x, y)= Jxy +x+xcos y. (a) Find fy - ở² f_ (b) Find дхду

A: f(x,y)=xy+x+x cos y

Q: Q7. Q7. Consider the vector-valued function 3ry ra(r, y. :) = (V=(* + s°), ) z(2² + y°), r2(r, y, z)…

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Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

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Q: Let a be a real number and f(x, y) = 5ax²y+ 4xy³. Let v = 3i – j and let Vf(x, y) denote the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Find the first order partial derivative with respect to y of the function f (x, y) = x³y² + 3æe".…

A: Differentiate given function with respect to y treat x as a constant.

Q: Gy Determin thle area between the curve 9 = x²+1 and y+ X = 7

A: Given: To determine the area between the curve y=x2+1 and y+x=7⇒ y=7-x

Q: Compute the partial derivative of f(z,y)=z'y with respect to a where: z(r, a)=re 3(r, s) = 8² +…

A: We have to find partial derivative here.

Q: If f(x,y,z) = 2x² − yz + xz², where x = 2 sint, y = t² − t + 1, and z = e−³t, find f't)

A: from chain rule of derivaties…

Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

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Q: Let f(x,y)=x•e. a. Compute all the first and second partial derivatives of f. b. Find the tangent…

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Q: Compute the partial derivative fa(, 4, 2) of the function f(2,4, 2) = yz' + 2 – 2 vy + * +2 y. O…

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Q: Let f(x, y) = e-o-Y 0 < x < ∞, 0 < y < ∞ be the joint pdf of X and Y. Find the pdf and cdf of X and…

A: The joint probability density function is given as below: f(x,y)=e-x-y ; 0&lt;x&lt;∞, 0&lt;y&lt;∞

Q: If f(z) = z4 = U(x, y) + iV (x, y), determine U and V. Verify that the C-R conditions are met at…

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Q: Suppose f(x, y, z) = xy cos z.Compute the partial derivative of f with respect to the variable y at…

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Q: Let y = f(x) be implicitly defined by xsin y = ycos x. Compute y' in terms of x and y.

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