1. A Bernoulli differential equation is one that takes the form y' + P(x)y = Q(x)y". (a) Classify the Bernoulli differential equation with n = 2, P(x) = 1, and Q(x) = x² as far as possible using the terms defined in the lecture notes, i.e. 1st-order, 2nd-order, linear, homogeneous, separable, etc.

Q: Use Cartesian coordinates to evaluate Jff v² av . D where D is the tetrahedron in the first octant…

A: We need to find the integral , ∭D y2 dV   where D is the tetrahedron in the first octant bounded by…

Q: Find the volume of the solid obtained by rotating about the x-axis the region bounded by the curve 2…

A: The answer is given below:

Q: 3. Determine the roots of y"" - 4y" + 3y = 0 a. 0, 1, 3 b. 0,-1, -3 c. 0, 1, -3 d. 0,-1, 3

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Q: Differentiate the function. P(w) = 2w² - 6w + 4 W

A: Given function is differentiated.

Q: Suppose h(x) = f(t)dt on the interval [0, 12], where f (t) is shown in the graph below. f (t) 8 10…

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Q: Solve the given initial value problem. O x³y²y³ = -18 O x³y² + xy³ = -18 Oxy² + x³ = -18 O x¹y² + y²…

A: So,it is non exact differential equation.

Q: Consider the differential equation y" - y' + 3y = f(t), such that y(0)=0 and y' (0) = -9 f(t) is…

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Q: For the following function, find the Taylor series centered at x = 5 and then give the first 5…

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Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

A: Here we have to solve this problem by using newtons law of cooling.

Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

A: Given problem:- 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a…

Q: Solve the given differential equation. All solutions should be found. dy e5 + 11y dx NOTE: Use c for…

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Q: 5. Use Cartesian coordinates to evaluate Jff ² av JIJ where D is the tetrahedron in the first octant…

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Q: 1)

A: Solution ) 1) in the first graph   We see that  In every value of x , y value is constant which is 2…

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Q: Evaluate the integral. a 6 dx ਚ 2 + a> 0

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Q: show that V(x, y) = x 'f (2x+y) is the genera Solution of : du 2X x av ах 1 ду

A: First, we find ∂v/∂x and ∂v/∂y  and substitute them in the given equation, if it satisfies the…

Q: Let F(x,y)=√√y-x, then answer the following ( (1) Find the function's domain (2) Find the function's…

A: According to our guidelines we can answer only one question or three subparts of a question.other…

Q: Given the graph of f(x) below. Determine the average rate of change of f(x) from x = -5 to x = -3.…

A: We need to find average rate of change.

Q: For each of the following ,find fx fy fxx fy fyx and fxy f(x, y) = x cos+ ye*. 2.f(x,y) = y²x¹e². 3.…

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Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

A: Let's find exact value of delta(Z).

Q: Given a second order differential equation dx 2x = e³t dt where t = 0, x = -5. Using Laplace…

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Q: 2. . If f(x) dx = 4 and 3g(x) dx = -9, evaluate [² [3f(x) + g(x)] dx

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Q: A В D ľ КIN 5л 2 (2 — 4sin(0) + 2 sin²(0)) d0 (2 - 4 sin(0) + 2 sin²(0)) d0 (1 — 2 sin(0) + sin²(0))…

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Q: 2. Two research assistants, Adi and Bea, review some data from an experiment. The number of pollu-…

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Q: The value of | Je A. -sin-¹ (ex) + C C. sin-¹ (e) + C dx 2x B.-sin-1 (e-2x) + C D. sin-¹ (e-2x) + C

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Q: adx + bxydy - ydx = -xyelny dy

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Q: Let F(x,y)=ln(x² + y2), then answer the following (1) Find the function's domain (2) Find the…

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Q: 2cos^2(?) sin3? dx

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Q: Evaluate the following Integral using integration by parts X CSC X S - dx CSCrCOU

A: Use by parts method of integration

Q: 4. Evaluate the double integral: Y SZ (Hint: Change the order of integration to dy dx.) dx dy. +1…

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Q: / If y" + 2y' F5y = e-Sint, y(0) = 0, y' (0) = 1

A: We solve the given differential equation using the higher order LDE techniques.

Q: Find the solution of the given initial value problem in explicit form. 7x y' = , y(0) = -9 y + x²y…

A: In this question, we will solve the given IVP.

Q: Evaluate sin (x) e-x dx by use Simpson's rule. h= 0.5

A: This is a problem related to integration part of the mathematics. Based on the general formula and…

Q: 5 Use Cartesian coordinates to evaluate [[[ v² av dV D where D is the tetrahedron in the first…

A: Please follow the next step.

Q: Evaluate each determinant.

A: A = -1523

Q: Find the first and second derivatives of the function. Check to see that your answers are reasonable…

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Q: e for (2x + 1) cos(x) dx. 14. Use integration by parts to evaluate

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Q: San 4h (x) dx = [ -3 y h 8 2 AN -3 10 4 -1/ -7 -7 7 x

A: From the graph, note that: ∫-30h(x) dx=-1 because area bounded by the curve h(x) is -1 in -3 to 0.

Q: 2. Find the total area under the curve f(x) = 2xe² from x = 0 and x = 5.

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Q: 6) The graph of g'(t) on the interval [0, 10] is shown below. If g(0) = 3, find g(10). g'(t) 4 0 t

A: Let's find value of g(10).

Q: Q4: A) For each of the following ,find fx fy fxx fyy fyx and fxy 1.f(x, y) = ln(2x + 3y). 2.f(x, y)…

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Q: 1. Find the Inverse Laplace Transforms of the following. 3s 2), 35544 2

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Q: 2 3) 9 = x ² sin x y વચ્ચે ઝ 4) y = sin x 1-2 cos x

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Q: 8 What type of association does the following represent: The value of y decreases as x increases A.)…

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Q: I. 4. Evaluate each determinant. 2 -5 2 -1 4

A: We have to find out determinant

Q: Find the volume of the region bounded above by the elliptical paraboloid z=8-3x²-4y² and below by…

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Q: 2. I. Evaluate each determinant. -4 3 -3 2

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Q: Find the solution of the given initial value problem. y = ²7y= y' cos t t-7 Y(T) = 0, t> 0 y(t) =

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Q: Solve the given differential equation. All solutions should be found. dy e5x+11y = dx NOTE: Use c…

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Q: Does the following series converge or diverge? 4√n Σ 3/2 10n +7n+7 n=1 O The series diverges. The…

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