Untitled

• Limit


  The value that a function approaches as the input variable gets closer and closer to a particular value
• Evaluating limits analytically


  1. Plug in a value close to the target value, but not the target value

  2. Factor the expression to cancel out terms that cause division by zero

  3. Use direct substitution if the expression does not have a fraction
• Evaluating limits graphically


  1. Identify the vertical line at the target value

  2. Approach the vertical line from the left side and note the y-value

  3. Approach the vertical line from the right side and note the y-value

  4. If the left and right limits match, the limit exists and is that value

  5. If the left and right limits do not match, the limit does not exist
• Types of discontinuities


  • Vertical asymptote - function value is undefined at that point
  • Jump discontinuity - graph does not connect at that point
  • Hole - removable discontinuity where the function value is undefined but the limit exists
• If a function has a zero in the denominator at a point, it creates a vertical asymptote at that point
• Vertical asymptotes and jump discontinuities are non-removable discontinuities
• Holes are removable discontinuities