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2.9: Homework- Algebraic Limits

Last updated

Oct 19, 2021
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- 2.8: Algebraic Limits
- 2.10: Instantaneous Velocity

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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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