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Algebraic Limits in Calculus

The document covers algebraic properties of limits including using tables and graphs to find limits. It contains examples of finding limits of functions as the variable approaches a value or infinity. Piecewise functions are also used to demonstrate finding limits.

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269 views1 page

Algebraic Limits in Calculus

The document covers algebraic properties of limits including using tables and graphs to find limits. It contains examples of finding limits of functions as the variable approaches a value or infinity. Piecewise functions are also used to demonstrate finding limits.

Uploaded by

lulu
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

5 Algebraic Properties of Limits


Calculus Name: _____________________________ CA #1
Use the table to find the given limits.
1.
lim 𝑓(𝑥) = 4 lim 𝑓(𝑥) = −3 lim 𝑔(𝑥) = 1 lim 𝑔(𝑥) = 6
→ → → →
( )
a. lim 𝑓(𝑥) + b. lim 𝑓(−𝑥)𝑔(𝑥)
→ →

Use the graph to find the given limits.


2.
y

a. lim 𝑓 𝑓(𝑥) =

→

         
x
b. lim 𝑓 𝑓(𝑥) =
→










Graph of 𝑓
Use the table to find the given limits.
3.
𝑓(3) = −2 lim 𝑓(𝑥) = 1
→

𝑔(3) = −4 lim 𝑔(𝑥) = 2


→

ℎ(3) = −6 lim ℎ(𝑥) = 3


→

( )
a. lim + ℎ(3) b. 𝑔(3) + lim ℎ(𝑥)𝑓(𝑥)
→ ( ) ( ) →

Use the piecewise functions to find the given values.


⎧ − , 𝑥 < −5 ⎧cos 2𝜃 , 𝜃<
⎪
4. 𝑔(𝑥) = 𝑥 − −5 ≤ 𝑥 < 2 5. ℎ(𝜃) = , <𝜃≤𝜋
⎨ ⎨
⎩√3 − 𝑥, 𝑥≥2 ⎪ sin , 𝜃≥𝜋
⎩
a. lim 𝑔(𝑥) b. lim 𝑔(𝑥)
→ → a. lim ℎ(𝜃) b. lim ℎ(𝑥)
→ →

c. lim 𝑔(𝑥) d. lim 𝑔(𝑥)


→ →
c. lim ℎ(𝜃) d. lim ℎ(𝑥)
→ →

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