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Sticky Note
lim x → 3 x² - 9/x - 3 = _____?
  1. 9
  2. 6
  3. 2
  4. None of these
Explanation

Let's evaluate the limit:

lim⁡x→3x2−9x−3

Step 1: Direct substitution gives 00, which is indeterminate. So, we simplify the expression.

Notice that x2−9=(x−3)(x+3). Therefore:

x2−9x−3=(x−3)(x+3)x−3=x+3(for x≠3)

Step 2: Now take the limit:

lim⁡x→3(x+3)=3+3=6

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