Calculus

Limit Notation

What is limit notation?

Limit notation is a way of describing the behavior of a function at a given location.
It helps us understand what happens to a function as the input approaches a specific value.

It is read as “the limit of (f(x)) as (x) approaches (a) is (b)”.

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Multiple Choice

Which is the correct notation for the "limit of f(x) as x approaches -1 is 0"

• $$\lim_{x\rightarrow-1}\ f\left(x\right)=0$$

• $$\lim_{x\rightarrow0}\ f\left(x\right)=-1$$

• $$\lim_{x\rightarrow1}\ f\left(x\right)=0$$

• $$\lim_{x\rightarrow0}\ f\left(x\right)=1$$

Multiple Choice

Which is the correct notation for the "limit of f(x) as x approaches 3 is 7"

• $$\lim_{x\rightarrow7}f\left(x\right)=3$$

• f(3)=7

• $$\lim\ f\left(3\right)=7$$

• $$\lim_{x\rightarrow3}\ f\left(x\right)=7$$

Fill in the Blanks

$\lim_{x\rightarrow5}\ f\left(x\right)=9$ in words

Fill in the Blanks

$\lim_{x\rightarrow2}f\left(x\right)=3$ in words

This time with graphs
(open desmos)

Multiple Choice

If f(x)=x^2+2x+4

what is $$\lim_{x\rightarrow-1}f\left(x\right)=?$$

• 7

• 0

• 3

• $$\pi$$

Multiple Choice

if f(x)=8^2-9

what is $$\lim_{x\rightarrow0}=?$$

• 2

• 9

• -9

• 0