Q I solve The Laplace equation 2 s² = u (0₁g) =0 X 4 (x, 0) 20 y (l,g) + u(l,g) U (X, 2) = 1 =0

Q: PART B: Let r2(t) = (vt² + 3, t – 4t + 1, t² – 1). Find equations for the tangent line to r2(t) at t…

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Q: dy/dt= y(y-0.5)(y-3)(sin(t2)-2) Determine the equilibria.

A: In this question, we Determine the equilibria. To explain why the Existence and Uniqueness theorem…

Q: The second directional derivative of f(x, y) is Du²f(x, y) = Du[Duf(x, y)]. 5 12 If f(x, y) = x³ +…

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Q: Find the tangential and normal components of the acceleration. r(t) = (t- 2)i + (In ( sec t)- 10)j +…

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Q: Graph these parametric equations on the TI and include screenshots x = 2t – 2 sin t, y = 2 – 2 cos t…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: Ydx - xdy + x(2 - y)dy = y? ey dy %3D

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Q: Use implicit differentiation to find an equation of the tangent line to the graph at the given…

A: As per the guideline, I am supposed to solve only first question from the given problems.

Q: y" + y " +y' + y = 1

A: A differential equation is said to be linear if no terms in it are formed by multiplication of two…

Q: Find the equations of the tangent lines to the traces of z=f(x,y)=16−3x^2−5y^2 at (−2,3). What is…

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Q: Find the linear approximation of the f(x, y) = Answer: f(x, y) ~ X x + y at the point (1,6).

A: To find the linear approximation of the function f(x, y) = x/(x + y) at the point (1, 6), we need to…

Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: [cost- sin t Q2) Determine whether x, = ,X1 = |cost| and x, = Lcos t] Co t sin t| are linearly…

A: For linearly independent , determinant of matrix should be non zero.

Q: Show that the function f(x; y; z) = 2z3- 3(x2+y2)z  satisfies the Laplace equation.

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Q: 8u?v? = 24 are solved for u and v as functions of x, y and z near the point P The equations xy² +…

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Q: H.W: 1. find the derivative of the function f(x, y, z)= xy + yz + zx ,at the point P(1,-1,2) in the…

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Q: DIfferentiate a) f(x)= cY X-4

A: a) fx=cx-43=cx-413 Differentiate with respect to x using the chain rule f'x=13cx-413-1…

Q: (a) Find the derivative of r(t) = (4 + t)i + tej + sin(5t) k. (b) Find the unit tangent vector at…

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Q: 9. At what point(s) on the circle x 2 + y? = 13 is its tangent line parallel to the line 3x – 2y = 6

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Q: A bug is flying along the curve x² + x³y³ + 6y² = 8 in an irregular way. dx m At the point (1, 1)…

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Q: (b) Determine whether u(x,t)= e' sinx is a solution to L

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Q: Which of these differentials is exact? (only one of them is exact) (1 – 2xy)dx + (x² + y²) dy O (22…

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Q: laplace(u(t-2)sin(t-2) )

A: laplace(u(t-2)sin(t-2) ) = e-2ss2+1

Q: 6. The equation 16 - 2 = 0 defines z as a function of x and y. Find az/dx and az/dy at the point (9,…

A: Given: The equation 6x+16y+2z-2=0 defines z as a function of x and y. To Find: ∂z∂x and ∂z∂y at the…

Q: Determine the integrating factor of z = 2xy – x %3D -2x 2e 2 2x e Option 3 O Option 1 None of the…

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Q: 4u?v? = 12 are solved for u and v as functions of x, y and z The equations æy² + 9xzcos(u) + ye" =…

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