Curriculum / Math / 11th Grade / Unit 9: Limits and Continuity / Lesson 8
Math
Unit 9
11th Grade
Lesson 8 of 9
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Lesson Notes
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Evaluate infinite limits and limits at infinity.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
Carla makes $${21}$$ of her first $${30}$$ free throws of the basketball season and then goes on a streak making every shot after that. Her free throw percentage is modeled by the function $$P(m)={{m+{21}}\over{m+{30}}}$$. As she takes more shots, what does her free throw percentage get closer to?
Use $${f(x)={{x+2}\over{x^2+4x+4}}}$$ to evaluate:
a. $${\lim_{x\rightarrow -2}f(x)=}$$
b. $${\lim_{x\rightarrow 2}f(x)=}$$
c. $${f(-2)=}$$
d. $${f(2)=}$$
e. $${\lim_{x\rightarrow \infty}f(x)=}$$
f. $${\lim_{x\rightarrow -\infty}f(x)=}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Use $${f(x)={{x^2-7x+12}\over{x-6}}}$$ to evaluate:
a. $${\lim_{x\rightarrow6}f(x)=}$$
b. $${f(6)=}$$
c. $${\lim_{x\rightarrow\infty}f(x)=}$$
d. $${\lim_{x\rightarrow-\infty}f(x)=}$$
Use $${g(x)=\left\{\begin{matrix} x+2, & x<-1\\ (x+1)^2+1, & -1\leq x <2 \\ -{1\over x}, & 2<x\leq4 \end{matrix}\right.}$$ to evaluate:
a. $${\lim_{x\rightarrow-\infty}g(x)=}$$
b. $${\lim_{x\rightarrow\infty}g(x)=}$$
Is this function $$g$$ continuous over the interval $${[0, 4]}$$? How do you know?
Next
Sketch functions given limits and continuity requirements.
Topic A: Limits and Continuity
Graph, write, and evaluate linear piecewise functions.
Use interval and function notation to describe the behavior of piecewise functions.
Sketch a slope graph from a linear piecewise function.
Find limits, including left- and right-hand limits, on a function given graphically.
Define continuity of functions and determine whether a function is continuous on a particular domain.
Write and evaluate piecewise functions algebraically and graphically using parent functions.
State and evaluate limits algebraically.
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