Question

find lim x->2 (x^2-4)/(x+2) using limit definition

Answer 1

lim(x->2){ x^2 - 4 / x + 2 } =

lim(x->2){ (x - 2) (x + 2) / (x + 2) } =

lim(x->2){ (x - 2) } = 2-2 = 0

Answer 2

Looks like you can just plug it in. The limit is equal to the function at that place since you're not dividing by zero.

Answer 3

i did it that way but my teacher want me to use the definition
\[\frac{ \frac{ (x+h)^2 }{ s+h+2 } -\frac{ x^2-4 }{ x+2 }}{ h }\]
i just need help simplifying...

Answer 4

if it was like this :
lim(x->2){ x^2 - 4 / x - 2 } =

lim(x->2){ (x - 2) (x + 2) / (x - 2) } =

lim(x->2){ (x + 2) } = 2+2 = 4

Answer 5

That's not the limit definition, that's the definition of a derivative.

Answer 6

derivative or W H A T