As you have written it, the expression approaches -∞ as x goes to 0.
What I think you really mean to ask is this:
[3-sqrt(x2+9)]/x2 as x goes to 0 which can be shown by L'Hospital's Rule to approach -1/6.
Find the limit as x approaches 0 of 3-[sqrt(x2+9)]/x2
As you have written it, the expression approaches -∞ as x goes to 0.
What I think you really mean to ask is this:
[3-sqrt(x2+9)]/x2 as x goes to 0 which can be shown by L'Hospital's Rule to approach -1/6.
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