These lessons will involve the students in investigating and understanding:
The concept of a limit
MIF: Limits to Infinity
MIF: Evaluating Limits
KA: Intro to limits
KA: Optional Extra Continuity introduction
An approach to the introduction of the number e using 1 lim 1
e = lim (1+1/n)n
n-> ∞ GEO: Visualise the limit
How to apply the rules for sums, products and quotients of limits (see 3.1)
KA: Limit properties
Khan Academy
Practice: Limits of combined functions
Find by inspection the limits of sequences such as
lim n/(n+1)
n-> ∞
MIF: Limits to Infinity
MIF: Evaluating Limits
Khan Academy
Practice: Limits at infinity of rational functions
lim rn , |r<1|
n-> ∞
Limits and continuity of functions through informal exploration
PM: Presentation Limits & Continuity
PM: Activity Sheet Informal Introduction to Limits and Continuity of Functions
Khan Academy
Practice: Approximating limits from graphs
Practice: Continuity and common functions
Practice: Infinite limits challenge
Derive the formula for the sum to infinity of geometric series by considering the limit of a sequence of partial sums
PM: Derive the formula for the sum to infinity of geometric series by considering the limit of a sequence of partial sums
Solve problems involving infinite geometric series such as recurring decimals
PM: Activity Sheets on Geometric Series from the T&L plan below
MIF: Recurring Decimal
KA: Infinite geometric series word problem: bouncing ball
KA: Infinite geometric series word problem: repeating decimal
Khan Academy
Practice: Infinite geometric series