2.9: Homework- Algebraic Limits

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Factor the following polynomials.
1. \(x^2 - 5x + 6\)
  \((x-2)(x-3)\)
  ans
2. \(x^2 + 2x - 63\)
  \((x-7)(x+9)\)
  ans
3. \(x^2 - 4xh + 4h^2\)
  \((x-2h)^2\)
  ans
If you’re doing a limit with a continuous function, like \(\lim_{x \to 3} 7x - 1\), how can you quickly solve this limit problem?
Plug it in!
ans
Compute the following limits algebraically.
1. \(\lim_{x \to 5} 2x^2 - 7x\)
  \(15\)
  ans
2. \(\lim_{x \to 2} \frac{(x-5)(x-2)}{x-2}\)
  \(-3\)
  ans
3. \(\lim_{x \to 3} \frac{x^2 - 6x + 9}{x - 3}\)
  \(0\)
  ans
4. \(\lim_{x \to -4} \frac{x^2 + 3x - 4}{x+4}\)
  \(-5\)
  ans
5. \(\lim_{x \to 2} \frac{x^3 - 6x^2 + 8x}{x-2}\)
  \(-4\)
  ans
6. \(\lim_{x \to w} x^2 + 5xw - w^2\)
  \(5w^2\)
  ans
7. \(\lim_{x \to h} \frac{x^2 - h^2}{x-h}\)
  \(2h\)
  ans

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