Unformatted text preview: x and cos x , but there are inﬁnitely many others.) Show that the function f also has this property. That is, show that f ( x +2 π ) = f ( x ) for all x . (This homework problem has nothing to do with inverse functions etc.; it’s just more practice in the art of proving things using deﬁnitions and known theorems.) Important note : For this assignment, and future assignments, avoid shorthands like “lim x → q 1 /x = √ + ∞ = + ∞ ” that pretend that + ∞ and∞ are numbers. Instead, say things like “As x → ∞ , 1 /x becomes arbitrarily large and hence so does its square root.” Please don’t forget to write down on your assignment who you worked on the assignment with (if nobody, then write “I worked alone”), and write down on your timesheet how many minutes you spent on each problem (this doesn’t need to be exact)....
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 Fall '11
 Staff
 Math, Calculus, Continuous function, Inverse function, Injective function, Multiplicative inverse

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