Question

lim as x approaches (1/2) from the right
x/2x-1
find the one sided limit

Answer 1

You may use l'Hopital's rule or some logic (In my work, I'll omitted saying "x -> 1/2 from the right"): \[ \lim \left( \dfrac {x}{2x+1} \right) = \dfrac {1}{2}. \]If you use l'Hoptial's rule, the derivative on the numerator is 1 and 2 on the denominator, making it \[ \boxed{\dfrac{1}{2}}. \]If you use logic, you can plug in some numbers and see that the argument is equivalent to: \[ \dfrac {x}{2x} = \boxed {\dfrac {1}{2}}. \]

Answer 2

Why is the limit not "unbounded" because of the asymptote

Answer 3

Because we are doing a one-sided limit.

Answer 4

I am not following at all. I guessed the limit was infinite

Answer 5

@Ahaanomegas Do we have an indeterminate form?

Answer 6

Also, where did the minus sign go?

Answer 7

@wio why is this not infinite

Answer 8

@Lills , looking at the graph, it is infinity or negative infinity depending which side you come from.

Answer 9

Coming from the right, it is positive infinity. You are correct.

Answer 10

@Ahaanomegas This is why we want to check for indeterminate form first! It might not work otherwise. In this case the limit doesn't exist unless you do a one sided limit.

Answer 11

Thank you @wio you helped keep me straight, i appreciate it

Answer 12

I stand corrected, wio. Thank you for helping me clear up my misconception. I keep making these types of mistakes on limits. Hopefully, that was the last time I did. :D

Thanks again!

Answer 13

Yeah I try to be careful on this site, but I've made lots of mistakes on my own homework and stuff.