Curriculum / Math / 11th Grade / Unit 9: Limits and Continuity / Lesson 8
Math
Unit 9
11th Grade
Lesson 8 of 9
Jump To
Evaluate infinite limits and limits at infinity.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
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
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?
Lesson 7
Lesson 9
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.
Sketch functions given limits and continuity requirements.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free