Set f(x) = xª for x ≥ 0 and f(x) = 0 for x < 0. For which values of a is f continuous at 0, and for which values of a is f differentiable at 0?

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A: As per the question we are given the system of equations as : 7x - 2y = 31 9x - 4y = 47 And we have…

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Q: 6. Evaluate the following real integrals by residue theorem 3 • I= 88 1527 dx (x²+1)(x² +9) ans 12

A: 6. To Evaluate: I=∫-∞∞dxx2+1x2+9

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Q: -11 -10 -9 -7 -8 -15 Submit Question -4 -3 -12 -16 + prot 15 -1 13- 11 10- 9 7 5 4 Jump to Answer 3…

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Q: 8. Given u = (1, 3, 2) and v = (3, 2, 4), find a) u + 2v b) ||u-v|| c) vector w if u + 2w = v

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Q: 3. [2 3 1-1221 and 8=6²-41 0 Lo Given A = B , show that (AB)T = BT AT.

A: Given matrices are A = 2101-21 ,  B = 23104-1

Q: 6th(v) 5 4 3 2 1 -6 -5 -4 -3 -2 -1 -1 -2 3 V 1 2 3 4 5 6 Find an equation for the graph above.

A: Sol:- It looks like graph of cosec(x) with some transformation  Graph of cosec(x)

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Q: Which of the following is a general solution to the following: x²y" + xy' + (36x² − 1) y = 0 A. y =…

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Q: Ўitsўіхву. ч. +8 Ця +7ўz FЧу; таўст бу, 2 * Чуа +2y=0 20

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Q: Considering u = u(x, y, z) find the solution of the equation: 8³ u əxəyəz = 0.

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Q: Find the general solution of the equation: anu dyn = 0.

A: Given equation is ∂nu∂yn=0   To Find: General solution of above equation.

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Q: 9. Consider the A defined on R, the set of all real numbers as V x, y € R, as x Ay ⇒x-y is rational.…

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Q: Determine the half-range sine series expansion of the following: f(t) = t² + t, A. B. C. D. y = 4 4…

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Q: Consider the following system of linear equations, 3x3 + 2x1 + X2 X1 + 2x₂ + 3x₂ 3x1 -2x1 -1 7 6 X2…

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Q: 2 Find the limit infimum and supremum of 2 XA = √√√ 1+n² √1tn 2A-5 write the complete solution.

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Q: Use Cauchy's Residue Theorem, where appropriate, to evaluate the given integral along the indicated…

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