omgitsana Group Title calculus: f(x)=(sin(x+1)/(x+1). does it have a vertical asymptote or a removeable discontinuity at x=-1?? 2 years ago 2 years ago

1. inkyvoyd

Well, how do you think you should start this problem?

2. omgitsana

well my main concern is idk if you can cancel the x+1 out

3. inkyvoyd

Of course you can't. Find the limits manually.

4. inkyvoyd

Or, you can use l'hopital's rule given that you have learned it.

5. lisapeajac

cannot cancel because it is not the exact same!!!

6. inkyvoyd

and, here's a hint: sin(a+b)=sin(a)cos(b)+sin(b)cos(a)

7. omgitsana

oh ok so it has vertical asymp?

8. inkyvoyd

Find the left and right hand limits. Are they the same?

9. inkyvoyd

$\lim_{x \rightarrow -1^-}=\lim_{x \rightarrow -1^+}$ is what I'm asking here.