Analysis and inequalities

[hidden flume]

As you can see the function in screenshot .
i want to ask that shouldnt there be an asymptote at 5 aswell ? Because as we notice , (x^2-4x-5) approaches 0 faster than the numerator (x-5) when lim x->5 so , why isnt there an asymptote ? This question was originally an inequality that i started analysis on afterwards.

[livid hound]

1. Wait patiently for a helper to come along.
2. Once someone helps you, say thank you and close the thread with: ```diff
   +close

[hidden flume]

Please ping me afterwards as i might not be online , sorry for inconvienences

Here is the screenshot ^^

[formal ginkgo]

it is not a question of how fast it approaches it

[hidden flume]

Then ?

[formal ginkgo]

as x gets close to 5, the (x-5) factor in denominator gets arbitrarily close to zero

but the (x-5) factor in numerator cancels it out

which is why you get a removable discontinuity instead of an asymptote

[hidden flume]

Ohh yeaaa , damn , that was a silly mistake

[formal ginkgo]

its alright, we all do these

[hidden flume]

Thanks btw

[formal ginkgo]

yw

[hidden flume]

thank @formal ginkgo

[wet bluff]

@storm drift has given 1 rep to @formal ginkgo

[hidden flume]

Bye

+close

[livid hound]

✅ Post closed

[formal ginkgo]

bye