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I need a Calculus help


Hello classmates,

May someone explain to me how to go about solving the limit of the equation below using figure 2 (which is attached)?

  • Limit of f(2x) as x approaches 1


The function f() is a rule that, given a number x assigns a number y. We don’t know what it’s graph would look like for numbers that are less than approximately x = -0.25 and numbers that are greater than approximately x = 4.25. But from the graph we see that f(0) = 1, that f(1) = 2, and that f(2) = 0. The graph also strongly suggests that we are to assume that the function f is continuous, so that we are to assume that lim of f(2x) as 2x approaches 2 is equal to f(2). That is lim of f(2x) as x approaches 1 is 0.

I don’t have the book, so I don’t know what has been said about notions such as the definition of the limit of a function or the definition of continuity. The notion of continuity requires that of a limit.

Please feel free to ask about anything I’ve said that might not seem clear.


I get it @rjl. Thank you so much.