Finding Limits from Graphs
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Objective
I can determine limits of functions graphically both one sided and two sided.
Part 1 of 3
Key concepts
3 concepts
- 1
A limit describes the value a function approaches as its input, x, gets arbitrarily close to a specific number.
- 2
A two-sided limit exists if and only if both the left-hand and right-hand limits exist and are equal.
- 3
If a graph exhibits a jump discontinuity or a vertical asymptote, the two-sided limit at that point does not exist.
Part 2 of 3
Practice
5 questions
What does it mean for a function to have a limit L as x approaches c, when determining this graphically?
Explain the relationship between one-sided limits and the existence of a two-sided limit at a particular x-value.
Part 3 of 3
Exit ticket
Quick comprehension check
“Consider a function f(x). As x approaches 2 from values less than 2 (x → 2⁻), the y-values of the function approach 4. As x approaches 2 from values greater than 2 (x → 2⁺), the y-values of the function approach 6. The function f(x) is undefined at x=2. Based on this information, determine the following limits: a) lim x→2⁻ f(x) b) lim x→2⁺ f(x) c) lim x→2 f(x)”
Sample answer included in the free materials
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