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anonymous
 one year ago
given that f(x)=(x^2)4x, evaluate the limit as x approaches 2 of (f(x)f(3))/(x2)
anonymous
 one year ago
given that f(x)=(x^2)4x, evaluate the limit as x approaches 2 of (f(x)f(3))/(x2)

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first you have to input f(x) into the equation, can you do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes, I got f(3)=1, and i input f(x) and f(3) into the equation and got ((x^2)4x3)/(x2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is correct, now you must factor the top, can you do that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0CORRECTION: the top portion is actually x^2  4x + 3 because you're subtracting f(3)

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0are you sure its f(3) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops, didn't notice that it was minus f(3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so that leaves me with (x1)(x3)/(x2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well... hmm f(3) is 3, f(3) is +3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do I get x2 out of the denominator? or do I leave it there and the answer is that the limit doesn't exist?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but I gather that's what amistre64 meant, using f(3), doesn't give us much relief on cancelling x2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0it's definitely f(3)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It does not exist, if you check the graph you can see that approaching 2, one side goes towards infinity, and one goes to +infinity

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0How about the lim = infinity?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's what I thought, thanks for confirming everyone!

amistre64
 one year ago
Best ResponseYou've already chosen the best response.0some foreshadowing tho: \[\lim_{x\to a}\frac{f(x)f(a)}{xa}\] is something that will come up alot later on

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0there is a vertical asymptote at x=2 and it is nonremovable if you need an explanation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@meagannlaurell the limit exists but at infinity, it is different from "does not exist"

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0In my class we interchange infinity and does not exist

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well looking at the graph, the two sides approach different infinities, one negative and one positive. So it would still be DNE, and yes, it is debatable as to whether DNE should equal /+infinity, but many classes do view them as interchangeable
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