Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Limit Rules, Exercises of Algebra

Cork College of Commerce (CCC)Algebra

an algebra trick and then continue finding the limit. ▻ indeterminant does not mean that the limit cannot be determined. It only means that the method you ...

Typology: Exercises

2021/2022

Uploaded on 08/05/2022

aichlinn
aichlinn 🇮🇪

4.4

(46)

1.9K documents

1 / 49

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Limit Rules
Useful rules for finding limits:
In the following rules assume k = constant
lim
x→ck=k
lim
x→ckf(x) = k lim
x→cf(x)
lim
x→cf(x) ±g(x) = lim
x→cf(x) ±lim
x→cg(x)
lim
x→cf(x) ·g(x) = lim
x→cf(x) ·lim
x→cg(x)
lim
x→c
f(x)
g(x) =limx→cf(x)
limx→cg(x)(6=0)
lim
x→c[f(x)n] = hlim
x→cf(x)in
lim
x→cP(x) = P(c) , P(x) is continuous around c, just plug-in
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13
pf14
pf15
pf16
pf17
pf18
pf19
pf1a
pf1b
pf1c
pf1d
pf1e
pf1f
pf20
pf21
pf22
pf23
pf24
pf25
pf26
pf27
pf28
pf29
pf2a
pf2b
pf2c
pf2d
pf2e
pf2f
pf30
pf31

Partial preview of the text

Download Limit Rules and more Exercises Algebra in PDF only on Docsity!

Useful rules for finding limits:

Useful rules for finding limits:

In the following rules assume k = constant

Useful rules for finding limits:

In the following rules assume k = constant

lim

x→c

k = k

lim

x→c

kf(x) = k lim

x→c

f(x)

Useful rules for finding limits:

In the following rules assume k = constant

lim

x→c

k = k

lim

x→c

kf(x) = k lim

x→c

f(x)

xlim→c f(x)^ ±^ g(x)^ =^ xlim→c f(x)^ ±^ xlim→c g(x)

Useful rules for finding limits:

In the following rules assume k = constant

lim

x→c

k = k

lim

x→c

kf(x) = k lim

x→c

f(x)

xlim→c f(x)^ ±^ g(x)^ =^ xlim→c f(x)^ ±^ xlim→c g(x)

xlim→c f(x)^ ·^ g(x)^ =^ xlim→c f(x)^ ·^ xlim→c g(x)

xlim→c

f(x)

g(x)

limx→c f(x)

limx→c g(x)( 6 =0)

Useful rules for finding limits:

In the following rules assume k = constant

lim

x→c

k = k

lim

x→c

kf(x) = k lim

x→c

f(x)

xlim→c f(x)^ ±^ g(x)^ =^ xlim→c f(x)^ ±^ xlim→c g(x)

xlim→c f(x)^ ·^ g(x)^ =^ xlim→c f(x)^ ·^ xlim→c g(x)

xlim→c

f(x)

g(x)

limx→c f(x)

limx→c g(x)( 6 =0)

lim

x→c

[f(x)n] =

[

lim

x→c

f(x)

]n

example

x^ lim→ 3

x^2 − 9 x − 3

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

x^ lim→ 3

x^2 − 9 x − 3

limx→ 3 x^2 − 9 limx→ 3 x − 3

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

x^ lim→ 3

x^2 − 9 x − 3

limx→ 3 x^2 − 9 limx→ 3 x − 3

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

x^ lim→ 3

x^2 − 9 x − 3

limx→ 3 x^2 − 9 limx→ 3 x − 3

0 0 is called an indeterminant form. When you reach an indeterminant form you need to try someting else.

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

x^ lim→ 3

x^2 − 9 x − 3

limx→ 3 x^2 − 9 limx→ 3 x − 3

0 0 is called an indeterminant form. When you reach an indeterminant form you need to try someting else.

x^ lim→ 3

x^2 − 9 x − 3

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

x^ lim→ 3

x^2 − 9 x − 3

limx→ 3 x^2 − 9 limx→ 3 x − 3

0 0 is called an indeterminant form. When you reach an indeterminant form you need to try someting else.

x^ lim→ 3

x^2 − 9 x − 3 = (^) xlim→ 3 (x − 3)(x + 3) (x − 3) = (^) xlim→ 3 (x + 3) =

example

x^ lim→ 3

x^2 − 9 x − 3

first try “limit of ratio = ratio of limits rule”,

x^ lim→ 3

x^2 − 9 x − 3

limx→ 3 x^2 − 9 limx→ 3 x − 3

0 0 is called an indeterminant form. When you reach an indeterminant form you need to try someting else.

x^ lim→ 3

x^2 − 9 x − 3 = (^) xlim→ 3 (x − 3)(x + 3) (x − 3) = (^) xlim→ 3 (x + 3) = 3 + 3 =