(b) (a)/ Use the calculus of residues to T (22 +9)2 6. -8 22 +1 dx x4 +1 T (b) %3D V2 dx (c) + 1)(z² + 4) (x2 + 1)(x2 + 4)
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- (D^5-3D^4+8D^3+16D^2-9D-13)y=0 nonhomogeneous undetermined coefficientsFind the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the linearization to estimate the value of f(2.1).Let y : R → R be the real-valued function defined on the real line, which is the solution of the initialvalue problemy' = −xy + x, y(0) = 2.Which statements are correct?a) The problem is not uniquely solvable.b) The solution y(x) contains an exponential function.c) limx→∞ y(x) = 1d) limx→∞ y(x) = 0
- Use field II to sketch the graphs of the solutions that satisfythe given initial conditions. a) y(0) = 1 b) y(0) = 2 c)y(0) = -1Find the general solution using Reduction of Order: y''+y'=cos 3xLet y : R → R be the real-valued function defined on the real line, which is the solution of the initialvalue problemy0 = −xy + x, y(0) = 2.Which statements are correct?a) The problem is not uniquely solvable.b) The solution y(x) contains an exponential function.c) limx→∞y(x) = 1d) limx→∞y(x) = 0
- f(x) = (x2-x-1) e-x is restricted to the domain x ≥ 0 and it has two critical points. One at x = 0 and the other at x = 3 At what value x does f(x) attain its maximum?A-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test. B-Find the value of a so that the function f (x) = xeax has a critical point at x = 3.Find the general solution using Reduction of Order: x2y''-xy'+y=0 y1=ln x