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Q: Write the following system of two second-order ODES as a system of four first-order ODES. Please…

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Q: Example: Evaluate J = S, e-**dx by using trapezoidal rule, n=10.

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Q: Find y(3) for y' = 1 + (x-y)2, y(2) = 1 by using Improved Euller's method. h = 0.5

A: Given  y'=1+x-y2 y2=1, h=0.5 We will find the value of y3

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Q: Use spherical coordinates. (a) Find the volume of the solid that lies above the cone o = n/3 and…

A: v=Center of mass  x¯=∫∫∫x dVVy¯=∫∫∫y dVVz¯=∫∫∫z dVV

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Q: suppose that S = [a, b] x {0} is a closed line segment %3D in R?. Show that H' (S) = b a.

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Q: 7. Suppose that f: R R is differentiable at c and that f(c) = 0. Show that g(x):= |f(x)| is…

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Q: Write the equation in spherical coordinates. (a) 5z2 = 8x2 + 8y2 (b) x2 + 3z2 = 7

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Q: Solve the following heat flow problem: Ut = 3uxx, 0< x < TT, 0<t <∞ u(0, t) = u(n, t) = 0,0 < t <0…

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Q: Let E be the region bounded above by z² + y² + z² = 10² , within z² + y² = 8² , below by the r®…

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Q: Evaluate the integral by changing to cylindrical coordinates. 16 - y2 xz dz dx dy 16-y2 Vx2+

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Q: 2. Use polynomial fitting to find a closed formula for the sequence (an)n e! E N: -2, –1,4,13,26,.

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Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. 2x y = (-2 + 3r)e¯*+2e² B В y = (-1+ 2x)e2* + 2e…

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Q: Find the area bounded by x=2y^2-4y+4 and x=y^2-2y+4.

A: To find the area between the curves x=2y2-4y+4, x=y2-2y+4.

Q: Find a root of an equation f (x)= –2x3 + 2x + 5 initial solution x0=1.5, using the Newton Raphson…

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Q: Determine whether the following series converge or diverge by using any appropriate test: 1+ k4/3 a)…

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Q: Find a particular solution to y" + 8y' + 16y : -7.5e 4t t² +1 Yp =

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Q: 3. Let (an)neN be a sequence in R defined as am = n+1 (i) Find inf(an) and justify your claim (ii)…

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Q: LShow that 91 is a pseudoprime to the base 3.

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Q: What is the expected value of spinning the following wheel? Each sector is the same size. 2 1 2. 3…

A: Use the following formula, to obtain the expected value. EX=∑xx·px Where px is the probability of x.