One of the critical points of f(x,y) – x² – 5y² + 10y – 27x is: O (3,1) O (3,1) O (1,1) None of these The double integral 2xy d4 over the rectangular region R- {(x,y) E RS, 0

Q: 1-6 Evaluate the integral by making the given substitution. 1. fcos 2x dx. u-2x 2. fx(2x²+3) dx, u=…

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Q: Use the transformation x = u/v, y = uv to evaluate the integral sum 4 p4/y [f" (² + y²) dx dy + [1²…

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Q: A clamped cubic spline S for a function f is defined by 5 5 + 2(x – 5) + (x – 5)² – 2(x – 5)³ S(x) =…

A: Let S1(x)=5+2(x-5)+x-52-2x-53 and S2(x)=a+b(x-6)+cx-62+dx-63 . Apply the following conditions of…

Q: 3.4.4 Sketch the domain of integration and evaluate 2x 1-x dy (a) dx (b) Laxf d.x 2 Xx² + y²² dx dy…

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Q: Prove that f (x, y) = (x + 2y)e*y has „no critical points.

A: Consider fx,y=x+2yexy. The critical points of two variable function exist at the points where both…

Q: 4. Find the double integral

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Q: 2 3 Evaluate the integral f S(x² + y)dydx. 0 1

A: Here given two variables in Integration

Q: L²³12x 20. Evaluate (a) -21 (d) 21 (g) The integral is divergent |2x - 4 dx (b)-5 (e) 5 (c) -3 (f) 3…

A: x=x,  x≥0-x,   x<0I=∫032x-4dx2x-4=0x=2∫xndx=xn+1n+1+c

Q: 1. Evaluate f[x(1-x*y² +xy )dydx. 01

A: To find the double integration

Q: Hence, for 0, 1 € Z2 there exists p(x, y), q(x, y) ≤ Z[x, y] such that g(p(x, y)) = p(0,0) = 0,…

A: I give the complete solution of original question.To prove that (x, y) and (2, x, y) are prime…

Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: Evaluate the integral (6x-y)dx + (x+6y)dy along the path C, defined as y = 16-x² from (0, 4) (4, 0).…

A: Answer: The solution is given below:

Q: Evaluate each of the following integrals over the given region D. sin2y (a) dxdy, D = {(x, y); 1 < x…

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Q: If f(x)=14-x^(2) and g(x)=\sqrt(x+31), compute g(f(3)). Simplify your answer as much as possible.

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Q: What is the Wronskian for y" + 3y = In x? & W 3 b. W = 3 c. W = V3cos 3x-V3 sin V3x d. W 3 cos 3x -3…

A: Here, the characteristic equation is m2+3=0. So,                         m2+3=0⇒m=±3 Thus, the…

Q: (c) y 8 2 (0, 1) y = e (2, e²)

A: We can use parametric form to find line integral .

Q: 68. Let Jr dx. %3D (a) Show that J1 = -e-x²/2. (b) Prove that Jn = -x"-le-x*/2 + (n – 1)Jn–2. %3D…

A: Solution is given below:

Q: 1. Evaluate 3 √² 13 0 |3x² - 12 dr.

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Q: Q2 Show that the region included between the cardioids r=a (1+ cos 0) r = a (1- cos 0) is given by:…

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Q: 6.F. F. dr along each path. (Hint: If F is conservative, the integration may be easier on an…

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