Question

Simple Piecewise Function, when is it continuous?

Answer 1

it'll be continuous when
\(\large \lim \limits_{x\rightarrow -1} \dfrac{x^2+5x+4}{x+1}=a\)
know how to find that limit ?

Answer 2

Oh i set them equal to each other? I never really understood limits, and continuity with piecewise functions.

Answer 3

Would i factor it to (x+1)(x+4)/(x+1). They would cancel out, and i would be left with (x+4)?

Answer 4

i took the limit to -1 and then equated them
and yes, that would be correct,

Answer 5

Alright, so where do i go from there?

Answer 6

\(\large \lim \limits_{x\rightarrow -1} x+4=a

\)
just plug in x= -1 !

Answer 7

Its undefined... hence the function saying x cannot = -1, thats why we're trying to find a.

Answer 8

ooh into that.

Answer 9

so a=3

Answer 10

yes! :)

Answer 11

Thanks : )

Answer 12

welcome ^_^