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Matthew ChoiMath6B-01-W15-CHENAssignment HW6 due 02/19/2015 at 11:59pm PST1.(1 pt) Suppose that you are told that the Taylor series off(x) =x5ex2aboutx=0 isx5+x7+x92!+x113!+x134!+···.Find each of the following:ddxx5ex2=d92.(1 pt) Suppose thatf(x)andg(x)are given by the powerseriesf(x) =6+3x+5x2+2x3+···andg(x) =6+2x+5x2+2x3+···.3.(1 pt) Represent the function 8ln(4-x)as a power series(Maclaurin series)f(x) =∞∑n=0cnxnc0=c1=c2=c3=c4=Find the radius of convergenceR=.4.(1 pt) Find all the values of x such that the given serieswould converge.