Subjects

Algebra 2

Geometric Series

Sequences, Series, Exponential Functions, and Logarithmic Functions - Class 11 Formulas, Worksheets, and Examples

Name: Knowunity
Brand: Knowunity

View

Sequences, Series, Exponential Functions, and Logarithmic Functions - Class 11 Formulas, Worksheets, and Examples

Mira

@miraa._noui

1,904 Followers

A comprehensive guide to sequences and series class 11 and related mathematical concepts, focusing on fundamental principles, formulas, and practical applications.

• The guide covers essential topics including sequences and series formulas, exponential functions, logarithms, and their properties
• Detailed explanations of arithmetic and geometric series, including partial sums and convergence conditions
• In-depth coverage of exponential functions and the number e, including real-world applications
• Comprehensive overview of logarithmic functions and properties, including graphing techniques and solving equations
• Practical examples and problem-solving strategies throughout the material

5/28/2023

720

<p>The study guide for Class 11 Sequences and Series covers the definition and notation of sequences, as well as various types of sequences

View

Page 2: Series and Summation Notation

This page delves into series calculations and sigma notation, providing fundamental properties and special series formulas.

Definition: A series is the sum of terms in a sequence, represented using sigma notation (Σ).

Vocabulary: Sigma notation includes:

Index of summation (x)
Lower bound (starting term)
Upper bound (last term)

Example: The sum of constants: Σc from x=1 to n equals c·n

Highlight: Key summation properties include:

Sum of functions: Σ[f(x) + g(x)] = Σf(x) + Σg(x)
Constant multiplication: Σcf(x) = cΣf(x)

View

Page 3: Advanced Series and Exponential Functions

This section covers arithmetic and geometric series, introducing exponential functions and their properties.

Definition: Exponential functions are those where the dependent variable increases/decreases by a constant multiple.

Example: Basic exponential function: y = a(b)ˣ

Highlight: For exponential functions:

Domain is (-∞,∞)
Range depends on 'a': (k,∞) if a>0; (-∞,k) if a<0

Vocabulary: In exponential functions:

b is the base/common ratio
a is the initial/critical value
h is horizontal shift
k is vertical shift

View

Page 4: The Number e and Logarithms

This final section introduces the number e and logarithmic functions, connecting them to real-world applications.

Definition: e is an irrational number (≈2.718) serving as the natural base for logarithms.

Example: Compound interest formula: A = P(1 + r/n)ⁿ

Highlight: Logarithmic functions are inverses of exponential functions, used when solving for variables in exponents.

Quote: "Logarithmic functions are the inverses of exponential functions"

Vocabulary: In compound interest:

A is account balance/future value
P is principal/initial deposit
r is annual interest rate
t is time in years
n is compounding frequency

View

Page 4: Exponential Functions and e

This section explores exponential functions and the number e pdf content, including practical applications.

Definition: The number e is an irrational number approximately equal to 2.718, often called Euler's number.

Example: Compound interest formula: A = P(1 + r/n)^(nt)

Highlight: The function y = e^x represents exponential growth with domain (-∞,∞) and range (0,∞).

View

Page 5: Logarithmic Functions

This page details logarithmic functions and properties worksheet concepts, focusing on graphing and transformations.

Definition: The general form of a logarithmic function is f(x) = alog_b(x-h) + k

Highlight: Key characteristics include:

Vertical asymptote at x = h
Domain: (h,∞)
Range: (-∞,∞)

View

Page 6: Properties of Logarithms

This section covers essential properties of logarithms examples and fundamental concepts.

Definition: Key logarithmic properties include base cancellation and product rules.

Example: log_2(2^3) = 3 (when bases are equal, the logarithm equals the exponent)

Highlight: The product rule states that log_a(MN) = log_a(M) + log_a(N)

View

Page 1: Fundamentals of Sequences

This page introduces the core concepts of sequences and their mathematical representation. The content focuses on both arithmetic and geometric sequences, providing essential formulas and notations.

Definition: A sequence is an ordered list of objects or numbers, with each item denoted as a "term".

Vocabulary: Domain of a sequence refers to consecutive list of terms (1, 2, 3, 4...n), while range represents the actual values in the sequence.

Example: For an arithmetic sequence 1, 3, 5, 7, the range is {1, 3, 5, 7}.

Highlight: Two key types of sequences are introduced:

Arithmetic sequences with constant difference (d)
Geometric sequences with constant ratio (r)

Quote: "The rule for arithmetic sequence: an = a₁ + d(n-1) OR an = an-1 + d"

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Subjects

Algebra 2

Geometric Series

Sequences, Series, Exponential Functions, and Logarithmic Functions - Class 11 Formulas, Worksheets, and Examples

Mira

@miraa._noui

1,904 Followers

A comprehensive guide to sequences and series class 11 and related mathematical concepts, focusing on fundamental principles, formulas, and practical applications.

5/28/2023

720

10th

Algebra 2

Page 2: Series and Summation Notation

This page delves into series calculations and sigma notation, providing fundamental properties and special series formulas.

Definition: A series is the sum of terms in a sequence, represented using sigma notation (Σ).

Vocabulary: Sigma notation includes:

Index of summation (x)
Lower bound (starting term)
Upper bound (last term)

Example: The sum of constants: Σc from x=1 to n equals c·n

Highlight: Key summation properties include:

Sum of functions: Σ[f(x) + g(x)] = Σf(x) + Σg(x)
Constant multiplication: Σcf(x) = cΣf(x)

Page 3: Advanced Series and Exponential Functions

This section covers arithmetic and geometric series, introducing exponential functions and their properties.

Definition: Exponential functions are those where the dependent variable increases/decreases by a constant multiple.

Example: Basic exponential function: y = a(b)ˣ

Highlight: For exponential functions:

Domain is (-∞,∞)
Range depends on 'a': (k,∞) if a>0; (-∞,k) if a<0

Vocabulary: In exponential functions:

b is the base/common ratio
a is the initial/critical value
h is horizontal shift
k is vertical shift

Page 4: The Number e and Logarithms

This final section introduces the number e and logarithmic functions, connecting them to real-world applications.

Definition: e is an irrational number (≈2.718) serving as the natural base for logarithms.

Example: Compound interest formula: A = P(1 + r/n)ⁿ

Highlight: Logarithmic functions are inverses of exponential functions, used when solving for variables in exponents.

Quote: "Logarithmic functions are the inverses of exponential functions"

Vocabulary: In compound interest:

A is account balance/future value
P is principal/initial deposit
r is annual interest rate
t is time in years
n is compounding frequency

Page 4: Exponential Functions and e

This section explores exponential functions and the number e pdf content, including practical applications.

Definition: The number e is an irrational number approximately equal to 2.718, often called Euler's number.

Example: Compound interest formula: A = P(1 + r/n)^(nt)

Highlight: The function y = e^x represents exponential growth with domain (-∞,∞) and range (0,∞).

Page 5: Logarithmic Functions

This page details logarithmic functions and properties worksheet concepts, focusing on graphing and transformations.

Definition: The general form of a logarithmic function is f(x) = alog_b(x-h) + k

Highlight: Key characteristics include:

Vertical asymptote at x = h
Domain: (h,∞)
Range: (-∞,∞)

Page 6: Properties of Logarithms

This section covers essential properties of logarithms examples and fundamental concepts.

Definition: Key logarithmic properties include base cancellation and product rules.

Example: log_2(2^3) = 3 (when bases are equal, the logarithm equals the exponent)

Highlight: The product rule states that log_a(MN) = log_a(M) + log_a(N)

Page 1: Fundamentals of Sequences

This page introduces the core concepts of sequences and their mathematical representation. The content focuses on both arithmetic and geometric sequences, providing essential formulas and notations.

Definition: A sequence is an ordered list of objects or numbers, with each item denoted as a "term".

Vocabulary: Domain of a sequence refers to consecutive list of terms (1, 2, 3, 4...n), while range represents the actual values in the sequence.

Example: For an arithmetic sequence 1, 3, 5, 7, the range is {1, 3, 5, 7}.

Highlight: Two key types of sequences are introduced:

Arithmetic sequences with constant difference (d)
Geometric sequences with constant ratio (r)

Quote: "The rule for arithmetic sequence: an = a₁ + d(n-1) OR an = an-1 + d"

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Download in

Google Play

Download in

App Store

4.9+

Average App Rating

15 M

Students use Knowunity

#1

In Education App Charts in 12 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User