Lim

[lilgrizz]

[tex]\lim_{x \to 0}x[/tex]

[Guest]

we can see that the limit exists on both sides:

[tex]\lim_{x \to 0^-}x=x^2=0[/tex] here [tex]0^-[/tex] refers to a number just smaller than [tex]0[/tex]
[tex]\lim_{x \to 0^+}x=x=0[/tex] here [tex]0^+[/tex] refers to a number just greater than [tex]0[/tex]

since the limit exists on both sides, [tex]\lim_{x \to 0}x=0[/tex]

[Guest]

we can see that the limit exists on both sides:

[tex]\lim_{x \to 0^-}x=x^2=0[/tex] here [tex]0^-[/tex] refers to a number just smaller than [tex]0[/tex]
[tex]\lim_{x \to 0^+}x=x=0[/tex] here [tex]0^+[/tex] refers to a number just greater than [tex]0[/tex]

since the limit exists on both sides, [tex]\lim_{x \to 0}x=0[/tex]

sorry forgot to mention that [tex]f(0)[/tex] is also 0. so the limit exists and is equal to 0