Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

oh ok so it has vertical asymp?

Answer 8

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

Answer 9

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