Concept explainers
To Find:
The main ideas of calculus.
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 17th 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
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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Chapter 18 Solutions
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