Determine whether on not the following limit exists. If, so compute the limit.
lim x->3 of sqrtx - 4 / x^3 +27
sqrt 3 - 4 / x^3 + 27 =
sqrt 3 -4 / 54 Is this correct?
I think so but wondered if it meant
lim x --> -3
and
sqrtx - 4 /( x^3 +27)
No its just 3
To determine whether the limit exists and compute it, we need to simplify the expression correctly first.
The given expression is:
lim x->3 of (sqrt(x) - 4) / (x^3 + 27)
To simplify this, we can substitute 3 into the expression and evaluate it directly. Let's do the substitution:
(sqrt(3) - 4) / (3^3 + 27)
= (sqrt(3) - 4) / (27 + 27)
= (sqrt(3) - 4) / 54
So, the expression is indeed
(sqrt(3) - 4) / 54
Therefore, your simplification is correct.