Introduction to Limits In Calculus

Introduction to Limits

[Graphically​]

By Abigail Makoski

1. What is a limit?

2. How do you read limit notation?

3. How do you interpret a limit from a graph?​

​Lesson Goals:

Imagine a short video here. There is a 5 minute animated video on YouTube that I like, but I don't have the paid version of Quizizz so I can't insert it here.

Multiple Choice

After watching the video, complete the following sentence:

The answer to a limit is always the ______ of a function at the given x value.

• the x value

• the intended y value

• the y value

• the intended x value

Fill in the Blanks

What is the limit as x approaches -4?

Fill in the Blanks

What is the limit as x approaches $\infty$  ?

Fill in the Blanks

What is the limit as x approaches $-\infty$  ?

Fill in the Blanks

What is the limit as x approaches 3?

​We have special notation to talk about limits.....

Fill in the Blanks

$\lim_{x\rightarrow0\ }f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow2\ }f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow-2\ }f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow-5^+\ }f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow-5^-\ }f\left(x\right)$  

Please copy into your notes:

Fill in the Blanks

$\lim_{x\rightarrow-4^+}\ f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow2^-}\ f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow2^+}\ f\left(x\right)$  

Open Ended

As x approaches 2 from the left the limit is -1, but as x approaches 2 from the right the limit is 1. What would the limit be if I didn't state a side?

Copy into your notes:

​If a limit Does Not Exist write DNE or dne

Let's try a few more to make sure you've got it!

Some text here about the topic of discussion

Fill in the Blanks

$\lim_{x\rightarrow0^+}\ f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow0^-}\ f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow3^-}\ f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow3^+}\ f\left(x\right)$  

Fill in the Blanks

$\lim_{x\rightarrow3^{ }}\ f\left(x\right)$  

1. What is a limit?

2. How do you read limit notation?

3. How do you interpret a limit from a graph?​

​Lesson Goals​

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Poll

Please rate how well you understand this lesson.