Limits and Continuity

1. Describe that a limit is the $${y-}$$value that a function gets arbitrarily close to as the function gets closer to a named $${x-}$$value. 
2. Use limit notation to describe limits from the left-hand, right-hand, and overall limit. 
3. Read the notation $${\lim_{x\rightarrow1^+}f(x)}$$ as “The limit of $$f$$ of $$x$$ as $$x$$ approaches $$1$$ from the right side.”
4. Read the notation $$\lim_{x\rightarrow1^-}f(x)$$ as “The limit of $$f$$ of $$x$$ as $$x$$ approaches $$1$$ from the left side.”
5. Read the notation $$\lim_{x\rightarrow1}f(x)$$ as “The limit of $$f$$ of $$x$$ as $$x$$ approaches $$1$$.”
6. Describe that if the left-hand and right-hand limits are not equal, the limit of the function at that point does not exist (DNE).

This lesson is aligned to the Learning Objectives and Essential Knowledge described in the College Board's AP Calculus AB and AP Calculus BC Course and Exam Description:

LO1.1A(b): EK1.1A1, EK1.1A2, EK1.1A3

LO1.1B: EK1.1B1

LO1.2A: EK1.2A1

Based on the graph below, which of the following is falase? Circle ALL that apply. Then, change the false statements into true statements.

A.  $${\lim_{x\rightarrow 1^+}h(x)\neq \lim_{x\rightarrow 1^-}h(x)}$$

B.  $${\lim_{x\rightarrow 1}h(x)\space \mathrm{exists}}$$

C.  $${\lim_{x\rightarrow 1^-}h(x)\neq h(1)}$$

D.  $${\lim_{x\rightarrow 1^+}h(x)\neq h(1)}$$