Given z = arctan (), Find az/ay

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Q: 7. Prove that if v >-1/2 ; p) = L{xvJ, (; = xı-at-a) H

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A: This is a problem of differential equation.

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Q: Let (a) Show that I is an ideal of Z × 2Z. (b) Use FIT for rings to show (Z × 2Z)/I ≈ Z₂. I= {(x, y)…

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Q: 2 SECTION A: MULTIPLE CHOICE QUESTIONS [40] dy 1. The complementary equation to +2 + 4y = 5e-3t is:…

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Q: x(y" + 1) + y² = 0.

A: we have to solve given problems:

Q: II. Solve the following problems. Enclose final answer. 4 4. Given z = Find az/ax x+y "

A: Solution:-

Q: ACTIVITY 1. Construct the truth table: (p^ q) → (~pv q) and determine whether it is a tautology,…

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Q: ? Exercise 15.2.3 The region bounded by the curves y = In z and y = e² in the interval [1, 2] is…

A: Area of region bounded by two curves y=fx (upper curve) and y=gx (lower curve) in the interval a≤x≤b…

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Q: 2. Consider the surface f(x, y) = x² + y² = x² + 2xy - y² - a) Find all critical points of f (Hint,…

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Q: 2. Consider the following first-order ODE: (a) Solve by hand with Euler's explicit method using h =…

A: Given the differential equation dydx=x-y with the condition y0=1 and step size h=0.4 Solve using…

Q: dy (c) Solve the differential equation x²e-x/x - y² + xy = dx = 0 with y(1) = 0.

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Q: Numerical Integration: r2 S 1 √x 1. dx

A: We have to evaluate the finite integral. ∫021xdx   Integration formula,  ∫xndx = xn+1n+1+c

Q: Suppose that there exists M> 0 and 8 >0 such that for all r = (a −8, a+6) \ {a}, f(x) = f(a)| ≤ Mx -…

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Q: Find the solution. y'= 1 + 3ytanx (A) 3y tan³x=c+ 3sinx-cos³x B 3y cos³x=c+3sinx - sin ³x D 3y…

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. In(x+1)³ 3. Lim 3 X→∞0 6x

A: Solution

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A: Given : A be any group and B be any subgroup of A. To prove : The right cosets of B partitions A.

Q: II. Find the general solution of the following differential equations. dy x+1 1) = dx 2(y+3) dy 2) =…

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Q: and conversely.

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Q: 3x y"+y= e¯x2 - 4x + 2x² + e³x 8-12x - 10x²

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the differential equation…

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Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

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Q: If A = 3xyz²i + 2xy³j-x²yzk and p = 3x² - yz, find (a) V-A, (b) A-Vq, (c) V.(Vo) at point (1,-1, 1).

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Q: Q.10. Let [a, b] be an interval of R. Let f:[a,b]→R be a function such that f is M-times…

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Q: By using exponential shift, which of the following is the solution for the differential equation…

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Q: Prove A by Contradiction

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Q: 2. Find the area bounded by the two curves y = x² - 6x²+ 8x and y = x² - 4x.

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Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: Problem 1 Find the Fourier transform of the given function. f(t) = 2A -t + A, 7sts ≤t≤ 0; T 2 2A T…

A: Fourier transform of a function ft with respect to t Fft=∫-∞∞ ft eist dt Where i is a complex unit…

Q: 3. The Critical Point of y = xe-x

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Q: Solve the following systems of linear equations by matrix. 2n+2v-2w+x-y=-2 u+3v+x-y=0 x+y=0…

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Q: 4:15 Homework: 2. Application of Integration Page 1 of 8 Save and complete later Find the…

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Q: Determine inverse z-transform of the following equations: 2² b. (2-1)(z-0.5)

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A: Option B is correct   I attach explanation in second step, i hope it will help you and you like my…

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Q: 18. The graph of 3[H(t2) - H(t-3)] is given by:

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