Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose level curves are solutions to the differential equation dy da +4x³ - Oy 3x + 5y²+2

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Q: 10. Give a combinatorial proof: For n ≥ 1 and k ≥ 1, (n)k = n · (n − 1)k-1.

A: To give: A combinatorial proof: For n≥1 and k≥1, k·nk=n·n-1k-1.

Q: EXERCISES 1.5 Is the function, whose graph is drawn in Fig. 7. continuous at the following values of…

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Q: 10. Evaluate indefinite integral xẻ dx S2-8x²² x

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Q: The problems 1) A particle of mass m is constrained to move on the cone 0 = 0o < 90°, where (r, 0,…

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Q: C = 6. (3C-2D)T 7. CTD + CDT 8. C²D² 9. det (CD+DC) 10. (CD – DC)-1 5 -2 1 0 -2 0 -4 1 10 -4 1 -11 2…

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Q: Find the area of the shaded region. -3 Am -1 y 3 x=y²-2² -3 y = 1 x = e 1 2 y = -1 3 4 X

A: Area of bounded region is calculated using double Integration is shown in next step

Q: A= 2 -4 5 ܂ * 3 -6 -6 8 ܕ ܗ ܕܝ 4 -3 6 -7 -1 -8 9

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Q: Problem 10.3 14 For the following u(x, y), show that it is harmonic and then find a corresponding…

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Q: CHAPTER 4 Gradient, Divergence, Curl ANSWERS TO SUPPLEMENTARY PROBLEMS 4.42. 10i-4j-16k, 2√93 4.43.…

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Q: 2.53 Prove the following identities when A and B are vectors and S, R, and T are second- order…

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Q: Exercise 2.23: Let X be a nonempty set. Define u*: P(X):→→ Ras: [0 If A is finite μ* (A) =- 1 If A…

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Q: (Remainder Theorem) Let F be field, a ∈ F, and f(x) ∈ F[x]. Then f(a) is the remainder in the…

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Q: (c) The solution of the initial value problem is OA. None of the given answers is correct OB. y(x) =…

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Q: 2. Given that P find a) | P+Q-R 2ax - ay - 2az; b) P Q X R c) Q = 4ax +3ay + 2az; C = cose PR -ax…

A: Since you have posted multiple questions, we will answer the first one. The rest questions you can…

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Q: (a) Find the differential equation satisfied by v(t) O A. dv V + dt 40 O B. dv V dt 40 None of the…

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Q: By Induction.Prove or disprove 4|7^2n +5

A: The statement is given by :       4|72n +5

Q: F(x, y, z)=ri+2yj + 3z k

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A: nither nor  means ~p∨q either or means  p∨q If and only if  means ↔ If..... then means → Not means ~

Q: 1. Solve d²y dx² dy 1 1 - 64² x + 9 = ²³² (√₁ ²²² = 2√5) e³x dx -x² 2√√x

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Q: 3. Show that the constant elasticity of substitution utility function U(x₁,x₂) = [α₂x₁° + α₂x²° ]¯½…

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Q: Problem 10.3 10 Evaluate the following limit. z² - 2iz - 1 lim z→i z4 + 2z² + 1

A: Given:  The given expression is limz→ iz2-2iz-1z4+2z2+1. To find: The value of the given limit.

Q: 4.18. Prove: (a) V• (A + B) = V• A + V• B, (b) V• (ФА) = (Vф)• A + ф(V• A). Solution (a) Let A =…

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Q: swer. Separate multiple answers, if there are multiple answers, by commas.)

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Q: choose the correct answer The Fibonacci sequence can be written as a “Rule”. First, the terms are…

A: We have to choose the correct answer The Fibonacci sequence can be written as a “Rule”. First, the…