dx : 2x-y dt %3D dy 3x - 2y + 8t %3D dt
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A: Taylor series for f(x) = e^x at x = -4
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Q: Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of…
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A: The value of the golden ratio: φ=1+52.
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Q: Use induction to prove the following formula holds for all n e N: 6.3+ 12 · 4 + 18 · 5 + + 6n(n + 2)…
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Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1
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Q: I. Use the flgure below to name one exampl B. F 3. Draw an example of a chord. Label Is JK. 4. Draw…
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Q: Use X = X + X, = eAtC + eAt e-As F(s) ds to find the general solution of the given system. d. X' = X…
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Q: 8:3 18. Coefficient of correlation between two points. From the followiag given sets of observations…
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Q: d?q (c) dt2 ' dt dq = t2 + 2t F(0) = 4 F'(0) = -2 %3D dx (d) + 2x = 2 F(0) = 0 %3D dt
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- Consider the system of linear equations in x and y. ax+by=ecx+dy=f Under what conditions will the system have exactly one solution?Find a system of two equations in three variables, x1, x2 and x3 that has the solution set given by the parametric representation x1=t, x2=s and x3=3+st, where s and t are any real numbers. Then show that the solutions to the system can also be written as x1=3+st,x2=s and x3=t.Find general solutions of the linear systems. If initial conditions are given, find the particular solution that satisfies them. x'' = -4x + sin t , y'' = 4x - 8y
- Solve the system of linear DE by elimination with initial conditionssolve the linear non-homogeneous system of equations with the given initial conditions.Now consider the case when the parameter varies slowly in time ,that is consider the system x'=a+x-x^3 and a'=-bx when b is so small. Sketch a typical solution to this system.
- Determine the values of the parameter s for which the system has a unique solution, and describe the solution.Find an example of a nonlinear equation, which is not solvable using any of the methods: separable, linear, solvable by a standard substitution (Bernoulli, homogeneous or linear combination) and which has y=x^2 as one of its solutions.Solve the system using the Jacobi method for 3 steps by taking x^0=0
- given that (x,y) > 0, find the equation for the non-zero x nullcline and y nullcline. What are the equilibrium points for the system? If you have an initial position of (3/2, 1/2) what will happen given the nullclines found?Solve the system ax - by - 2cz = 21, ax + by + cz = 0 and 2ax - by + cz = 14 for (x, y, z) in terms of the nonzero constants a, b, and c.The system has a single critical point. Find and classify this critical point as to type and stability. dx/dt = 2x-2y+4 dy/dt = -7x-3y-24