Day 44 - Limits at Infinity - 10.20.14

Updates
  • Hand back Quiz 7
  • Go over Quiz 7
    • Average = 78%
Bell Ringer
  • Concavity and Inflection Points

  1. Find all intervals on which f(x) = (x + 1) / (x - 3) is concave upward.

    1. (1. ∞)

    2. (-∞, ∞)

    3. (-∞, 3)

    4. (3, ∞)

    5. none of the above

  2. Find all points of inflection: f(x) = x4 / 12 - 2x2 + 15

    1. (2, 0)

    2. (2, 0); (-2, 0)

    3. (0, 15)

    4. (2, 25/3); (-2, 25/3)

    5. none of these

  3. What is the horizontal asymptote for the following: f(x) = 4 - 6 / x3?

    1. y = -4

    2. y = 0

    3. x = 4

    4. y = 4

    5. none of the above

  4. What is the horizontal asymptote for the following: f(x) = (3x - 2) / (6x - 1)

    1. y = ½

    2. y = -½

    3. x = ½

    4. y = 3

    5. none of the above
Review
Lesson
Exit Ticket
  • Posted at the end of the block.
Lesson Objective(s)
  • How can limits at infinity be calculated?
  • How are limits at infinity related to horizontal asymptotes?
Standard(s)
  • APC.8

    • Apply the derivative to solve problems.

      • Includes:

        • ​analysis of curves and the ideas of concavity and monotonicity

        • optimization involving global and local extrema;

        • modeling of rates of change and related rates;

        • use of implicit differentiation to find the derivative of an inverse function;

        • interpretation of the derivative as a rate of change in applied contexts, including velocity, speed, and acceleration; and

        • differentiation of nonlogarithmic functions, using the technique of logarithmic differentiation.*

Mathematical Practice(s)
  • #1 - Make sense of problems and persevere in solving them
  • #2 - Reason abstractly and quantitatively
  • #5 - Use appropriate tools strategically
  • #6 - Attend to precision
  • #8 - Look for and express regularity in repeated reasoning
Past Checkpoints
  • Extrema (page 169)
    • A - #4
    • B - #6
    • C - #18
    • D - #22
    • E - #34
  • Rolle's Theorem (page 176)
    • F - #4
    • G - #10
    • H - #26
  • Mean Value Theorem (page 176-177)
    • I - #34
    • J - #42
    • K - #44
  • Increasing/Decreasing Functions (page 186)
    • L - #6
    • M - #20
    • N - #44
    • O - #48
  • Concavity and Points of Inflection (page 195)
    • P - #6
    • Q - #16
    • R - #18
    • S - #20
    • T - #24
    • U - #32
    • V - #38
    • W - #52