SolveMathAI

Find the limit as x approaches 3 of (x^2 - 9)/(x - 3)

Worked through step by step. More limits.

Answer
6\boxed{6}

Substituting x=3x = 3 directly into the original expression yields a 00\frac{0}{0} indeterminate form, but algebraic simplification reveals the correct limit of 66.

Problem: Find the limit lim⁡x→3x2−9x−3\lim_{x \to 3} \frac{x^2 - 9}{x - 3}.

Steps

  1. Factor the numerator
    lim⁡x→3(x−3)(x+3)x−3\lim_{x \to 3} \frac{(x - 3)(x + 3)}{x - 3}
  2. Cancel the common factor
    lim⁡x→3(x+3)\lim_{x \to 3} (x + 3)
  3. Substitute x=3x = 3
    3+3=63 + 3 = 6

Generated by SolveMath AI and kept here so the next person asking gets it instantly. AI can make mistakes, so check anything that matters.

Solve your own

Same solver, same steps, no account.

Enter to solve · Shift+Enter for a new line

  • Free
  • No account
  • Every step shown
  • Arithmetic to calculus

More solved problems

Limits solver →
Find the limit as x approaches 0 of sin(x)/xFind the limit as x approaches infinity of (3x^2 + 2x)/(5x^2 - 1)Find the limit as x approaches 2 of (x^2 - 4)/(x - 2)Find the limit as x approaches infinity of 1/xFind the limit as x approaches 0 of (e^x - 1 - x)/x^2Find the limit as x approaches 0 of (1 - cos x)/x