The main ideas of calculus.

Question

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Answer 1

Question

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.

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Answer 2

Question

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.

Answer 6

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.

Answer 7

Chapter 18.CR, Problem 1CR

To determine

To Find:

The main ideas of calculus.

Answer 8

Expert Solution & Answer

Answer to Problem 1CR

Solution:

The main ideas of calculus are Limits, Derivatives and Integrals.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Calculus is the mathematics of motion and change, which is why calculus is a prerequisite for many courses.

The development of calculus in the 17^th century by Newton and Leibniz was the result of their attempt to answer some fundamental questions about the world and the way the things work. These investigations led to two fundamental concepts of calculus, namely the idea of a derivative and that of an integral. The breakthrough in the development of these concepts was the formulation of a mathematical tool called a limit.

1. Limit: The limit is a mathematical tool for studying the tendency of a function as its variable approaches some value. Calculus is based on the concept of limit.

2. Derivative: The derivative is defined as a certain type of limit, and it is used initially to compose the rates of change and slopes of tangent lines to curves, The study of derivatives is called differential calculus. Derivatives can be used in sketching graphs and is finding the extreme values of the functions.

3. Integral: The integral is found by taking a special limit of a sum of terms, and the study of this process is called integral calculus. Area, volume, arc length, work, and hydrostatic force are a few of the many quantities that can be expressed as integrals.