Homework:  Algebraic Limits

11 Homework: Algebraic Limits

Factor the following polynomials.
1. [latex]x^2 - 5x + 6[/latex]
  
  [latex](x-2)(x-3)[/latex]
  
  ans
2. [latex]x^2 + 2x - 63[/latex]
  
  [latex](x-7)(x+9)[/latex]
  
  ans
3. [latex]x^2 - 4xh + 4h^2[/latex]
  
  [latex](x-2h)^2[/latex]
  
  ans
If you’re doing a limit with a continuous function, like [latex]\lim_{x \to 3} 7x - 1[/latex], how can you quickly solve this limit problem?

Plug it in!

ans
Compute the following limits algebraically.
1. [latex]\lim_{x \to 5} 2x^2 - 7x[/latex]
  
  [latex]15[/latex]
  
  ans
2. [latex]\lim_{x \to 2} \frac{(x-5)(x-2)}{x-2}[/latex]
  
  [latex]-3[/latex]
  
  ans
3. [latex]\lim_{x \to 3} \frac{x^2 - 6x + 9}{x - 3}[/latex]
  
  [latex]0[/latex]
  
  ans
4. [latex]\lim_{x \to -4} \frac{x^2 + 3x - 4}{x+4}[/latex]
  
  [latex]-5[/latex]
  
  ans
5. [latex]\lim_{x \to 2} \frac{x^3 - 6x^2 + 8x}{x-2}[/latex]
  
  [latex]-4[/latex]
  
  ans
6. [latex]\lim_{x \to w} x^2 + 5xw - w^2[/latex]
  
  [latex]5w^2[/latex]
  
  ans
7. [latex]\lim_{x \to h} \frac{x^2 - h^2}{x-h}[/latex]
  
  [latex]2h[/latex]
  
  ans

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