CAL01

• What is the limit of the function \( f(x) \) as \( x \) approaches -2?


  lim \( x \to -2 f(x) = -3 \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 0?


  lim \( x \to 0 f(x) = 1 \)
• What is the limit of the function \( f(x) \) as \( x \) approaches -1?


  lim \( x \to -1 f(x) = -2 \)
• What is the limit of the function \( f(x) \) as \( x \) approaches -4?


  lim \( x \to -4 f(x) = 1 \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 1 from the left?


  lim \( x \to 1^- f(x) = +\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 1 from the right?


  lim \( x \to 1^+ f(x) = +\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 1?


  lim \( x \to 1 f(x) = +\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 0?


  lim \( x \to 0 f(x) = -1 \)
• What is the limit of the function \( f(x) \) as \( x \) approaches \( \frac{1}{2} \) from the left?


  lim \( x \to \frac{1}{2}^- f(x) = -\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches \( \frac{1}{2} \) from the right?

  lim \( x \to \frac{1}{2}^+ f(x) = +\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches \( \frac{1}{2} \)?


  lim \( x \to \frac{1}{2} f(x) = DNE \)
• What is the limit of the function \( f(x) \) as \( x \) approaches -2 from the left?


  lim \( x \to -2^- f(x) = +\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches -2 from the right?


  lim \( x \to -2^+ f(x) = -\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 2 from the left?

  lim \( x \to 2^- f(x) = -\infty \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 2?


  lim \( x \to 2 f(x) = DNE \)
• What is the limit of the function \( f(x) \) as \( x \) approaches -2?

  lim \( x \to -2 f(x) = DNE \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 2 from the right?


  lim \( x \to 2^+ f(x) = 1 \)
• What is the limit of the function \( f(x) \) as \( x \) approaches 2 from the left?


  lim \( x \to 2^- f(x) = 3 \)
• What is the method used to evaluate the limit of the function \( \frac{2x^2 - 25}{2x - 5} \) as \( x \) approaches 5?

  Factor the expression and simplify
• What is the limit of the function \( \frac{2(2x + 5)(2x - 5)}{2x - 5} \) as \( x \) approaches 5?

  10
• What is the method used to evaluate the limit of the function \( \frac{2x^2 - 3x + 1}{2x - 1} \) as \( x \) approaches 1?


  Factor the expression and simplify
• What is the limit of the function \( \frac{(2x - 1)(x - 1)}{2x - 1} \) as \( x \) approaches 1?


  • 1/2
• What is the method used to evaluate the limit of the function \( \frac{x^2 - 2x - 8}{x^2 - x - 12} \) as \( x \) approaches 4?

  Factor the expression and simplify
• What is the limit of the function \( \frac{(x - 4)(x + 2)}{(x - 4)(x + 3)} \) as \( x \) approaches 4?

  6/7
• What is the method used to evaluate the limit of the function \( \frac{2x + 4}{\sqrt{x} + 2} \) as \( x \) approaches 7?

  Substitute directly
• What is the limit of the function \( \frac{2(7) + 4}{\sqrt{7} + 2} \) as \( x \) approaches 7?

  6
• What is the method used to evaluate the limit of the function \( \frac{x^6 - 1}{x^4 - 1} \) as \( x \) approaches -1?


  Factor the expression and simplify
• What is the limit of the function \( \frac{(x^2 - 1)(x^4 + x^2 + 1)}{(x^2 - 1)(x^2 + 1)} \) as \( x \) approaches -1?

  3/2
• What is the method used to evaluate the limit of the function \( \frac{x - 4}{\sqrt{x} - 2} \) as \( x \) approaches 4?

  Rationalize the numerator
• What is the limit of the function \( \frac{(x - 4)(\sqrt{x} + 2)}{x - 4} \) as \( x \) approaches 4?

  4
• What is the method used to evaluate the limit of the function \( \frac{\sqrt{x} + 3 - \sqrt{3}}{x} \) as \( x \) approaches 0?


  Rationalize the numerator
• What is the limit of the function \( \frac{x}{x(\sqrt{x} + 3 + \sqrt{3})} \) as \( x \) approaches 0?


  \(\frac{1}{2\sqrt{3}}\)
• What is the method used to evaluate the limit of the function \( \frac{1}{x - 2} \) as \( x \) approaches 0?

  Substitute directly
• What is the limit of the function \( \frac{\sqrt{x} + 4 - 2}{x} \) as \( x \) approaches 0?

  \(\frac{1}{8}\)
• What is the method used to evaluate the limit of the function \( \frac{4}{x^2 - 1} + \frac{2}{x + 1} \) as \( x \) approaches 0?

  Combine fractions and simplify
• What is the limit of the function \( \frac{4}{0 - 1} + \frac{2}{0 + 1} \) as \( x \) approaches 0?

  2
• What is the method used to find vertical asymptotes of the function \( f(x) = \frac{4x^2 - 3x + 2}{x^2 - 3x + 2} \)?

  Find the roots of the denominator
• What are the vertical asymptotes of the function \( f(x) = \frac{4x^2 - 3x + 2}{x^2 - 3x + 2} \)?

  x = 1 and x = 2
• What is the method used to find horizontal asymptotes of the function \( f(x) = \frac{4x^2 - 3x + 2}{x^2 - 3x + 2} \)?


  Evaluate the limit as \( x \to \infty \)
• What is the horizontal asymptote of the function \( f(x) = \frac{4x^2 - 3x + 2}{x^2 - 3x + 2} \)?

  y = 4