Question

lim
x→−5

5 − |x|/5 + x

Find the limit of x
Thank you for your help!

Answer 1

(if it exists)

Answer 2

Approach x = -5 from the left and from the right. If you are approaching the same value, the limit does exist. It might help to plot some points to see what's going on. The idea is that the limit can exist, even if the expression isn't solvable at that precise point

Answer 3

Yes.. I do get that part, but I dont have a graph or anything?? Im not sure how I should approach it

Answer 4

I keep getting 0 ..

Answer 5

I haven't worked it, but the limit could be 0. Are you thinking that's wrong?

Answer 6

Is the original problem a fraction where 5-|x| is in the numerator and (5+x) is the denominator?

Answer 7

yes!

Answer 8

I am plugging in the -5.. are you getting a zero as well?

Answer 9

you can't just plug in -5, because the denominator would be zero and the function would be undefined

Answer 10

oh..

Answer 11

hmm..

Answer 12

I GOT IT! it's 1

Answer 13

the negative absolute value of x... is -x so.. haha yay

Answer 14

If you sub in values for x like -10, -9, etc you always get f(x) = 1, right?

And if you sub in values for x like 0, -1, -2, -3 etc you still get f(x) = 1

but at x = -5, it's undefined. However, the limit as you approach that point is 1 because the f(x) values on both sides, no matter how close you want to go, are still = 1

Answer 15

good work... didn't see you already had it :)

Answer 16

:) thanks!!!!

Answer 17

thank you too!~