- anonymous

The graph of a function f is given above.

- katieb

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- anonymous

What is \[\lim_{x \rightarrow 2}\frac{ x }{ f(x)+1 }\]

- dinamix

f(x) equal what mate

- anonymous

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## More answers

- Vocaloid

well, start by finding
f(2)

- anonymous

f(2)=-1

- dinamix

its infinity this lim but dont know + or -

- dinamix

its + infinity

- anonymous

How do I know if it's positive or negative Infiniti?

- amistre64

1 - (something smaller than 1) is a positive number; and x=2 is a positive number
+/+ = +

- amistre64

|dw:1440260968991:dw|

- anonymous

I forgot to make the bottom of the graph negative oops :(

- anonymous

|dw:1440261046439:dw|

- amistre64

you see that for say x between 1 and 3,
that the top of the setup is positive
and that the bottome part: f(1,3) + 1 is just the same as: 1 - (a fraction) is positive

- anonymous

How did you get f(1,3) +1 and 1-(a fraction)?

- amistre64

i glossed over x=2 :) other than that
you see that f(x) is a value between 0 and -1 right?

- amistre64

-a + 1 = 1 - a

- amistre64

and saying "a fraction" is lazy as well, since the values are both rational and irrational.

- anonymous

Oh ok :) so f(1,3) means those are the x values that cross on 0 and that's why you add 1?

- amistre64

f(x) + 1 is the bottom of your setup
and if we just focus on the values between 1 and 3; f(1,3) just denotes all the values we can conceive of yes

- amistre64

x = (1,3) includes x=2
f(1,3) includes all the values that x produces along the stated domain

- anonymous

Ohh ok :)

- anonymous

So do I solve for 1 first, and the 3?

- amistre64

no, i was just making an observation
the value of the bottom, when x=2, is 0 since f(2) = -1
now, the limit is defined if the value that is approached from the left and right of x=2 is the same.
so we observe that for a small enough region around x=2, the top is always positive, and the bottom is always positive; therefore, we approach the same infinity (+inf).
but in may classes, infinity is still classified as DNE

- anonymous

Ohh ok I understand now :)

- amistre64

good luck

- anonymous

Thank you!!!!

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