Evaluate the integral 1 x3 dx. 1+ x2 0.

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A: Convergence of the series

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Q: 2. Prove that a free group of rank > 1 has trivial center.

A: Given:Prove that a free group of rank>1 has trivial center

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A: Given: Contour map for a function f is shown below: To find: fy4, 29.

Q: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

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Q: Example 10.28. Solve the differential equations dy = 1+ xz, dx dz - xy for x 0.3, dx using fourth…

A: we need to use runge-kuta fourth order method.

Q: Use the graph to compute the quantities asked for. ... -3 -2 A. lim Ax) = %3D B. lim (x) = %3D

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Q: I Example 10.18. Using Runge-Kutta method of fourth order, solve for y at x = 1.2, 1.4 dy. 2xy + e*…

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Q: Find a possible formula for the function in the figure below. P = (0,2) Q = (8,0) ) -16 -12 -8 12 16…

A: Given is a figure of a function   Given that graph of the function passes through P(0,2),  Q(8,0)…

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A: Introduction: A transformation alters a fundamental function by applying preset procedures to it.…

Q: Find the flux of F across S, F.N dS where N is the upward unit normal vector to S. F(x, y, z) = xi +…

A: The given integral is ∬SF·N ds , where S: z=a2-x2-y2  and F(x,y,z)=x i^ + y j^- 2z k^ .....1. To…

Q: Consider the following function. f(x) = 2 sin(x) + 2 cos(x), [0, 2n] Find f'(x). f'(x) Find f"(x).…

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Q: Find the Taylor polynomials p1, .. P4 centered at a = 0 for f(x) = 3 cos (6x).

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Q: Graph the vector function 7(t) = (t3 + 1)ĩ + tj:

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