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Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0.
(a) If (xn) converges to x, show that (|axn + b|) converges to |ax + b|.(b) Give an instance , with brief justication, where (|xn|) converges but (xn) does not.(c) If (|xn|) converges to 0, elustratethat (xn) converges to 0.
In (a) you need to use only the denition of convergence and no other limit theorems.
The equation -2x^2-kx-2=0 has two different real soultions. find the set of possible values for k.
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Question: Find all third order partial derivatives for the function F(x,y)= log xy+ e (x+y) -x/y.
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