Use the residue theorem to prove that: dx x√x² - 1 || Π - 2 1

I need help with Real Analysis HW

Let f(x) = 2xc + 1 C + 3x --9 8 Oc==3 4 Oc=21/20 Oc=1 Oc==3 Determine the value of c so that x = is a vertical asymptote of f(x).

1 The coordinate of the invariant points when f(x) = -x + 2 is transformed to y = √√(x) are: (a,b) and (c,d). State the values of a,b,c and d in the answer box (no spaces, no commas: abcd)

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Suppose that Pr[A|B]=7/13, Pr[B|A]=7/11, and Pr[A′]=10/21. Find Pr[A∩B′].  Write answer as a fraction.

dx ~∞ (x²+4)² 8 4) Using the Residue Theorem, show that S I 16

Let be the square root function defined by 1 z² = √√√|z|e 2 Show that this function is discontinuous at the point Zo = -1 iArg(z)

Let f(x) = 5x4+ 3x3+ 1 and g(x)= 3x2+ 2x+ 1 in Z7 [ x ]. Determine the quotient ad remainder upon dividing f(x) by g(x).

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