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In this section you'll find study materials for calculus help. Use the links below to find the area of calculus you're looking for help with. Each study guide comes complete with an explanation, example problems, and practice problems with solutions to help you learn calculus.

Study Guides

showing 21 - 30 of 94
  • 21.

    l’Hôpital’s Rule Help

    Introduction to l’Hôpital’s Rule Consider the limit

    Source: McGraw-Hill Professional
  • 22.

    Other Indeterminate Forms Help

    Introduction to Other Indeterminate Forms By using some algebraic manipulations, we can reduce a variety of indeterminate limits to expressions which can be treated by l’Hôpital’s Rule. We explore some of these techniques in this section.

    Source: McGraw-Hill Professional
  • 23.

    Improper Integrals Help

    Introduction to Improper Integrals The theory of the integral that we learned earlier enables us to integrate a continuous function f ( x ) on a closed, bounded interval [ a, b ]. See Fig. 5.1. However, it is frequently convenient ...

    Source: McGraw-Hill Professional
  • 24.

    More on Improper Integrals Help

    Introduction to More on Improper Integrals Suppose that we want to calculate the integral of a continuous function f ( x ) over an unbounded interval of the form [ A , +∞) or (−∞, B ]. The theory of the ...

    Source: McGraw-Hill Professional
  • 25.

    Indeterminate Forms Practice Test

    Review the following concepts if needed: l’Hôpital’s Rule Help

    Source: McGraw-Hill Professional
  • 26.

    Logarithm Basics Help

    Introduction to Logarithm Basics There are two types of functions: polynomial and transcendental. A polynomial of degree k is a function of the form p ( x ) = a 0 + ...

    Source: McGraw-Hill Professional
  • 27.

    Derivative of Logarithm Function Help

    The Logarithm Function and the Derivative Now you will see why our new definition of logarithm is so convenient. If we want to differentiate the logarithm function we can apply the Fundamental Theorem of Calculus:

    Source: McGraw-Hill Professional
  • 28.

    Exponential Basics Help

    Exponential Basics Examine Fig. 6.4, which shows the graph of the function f(x) = ln x, x > 0.

    Source: McGraw-Hill Professional
  • 29.

    Exponentials with Arbitrary Bases Help

    Introduction to Exponentials with Arbitrary Bases We know how to define integer powers of real numbers. For instance

    Source: McGraw-Hill Professional
  • 30.

    Derivative and Integral of Logarithm Help

    Introduction to Derivative and Integral of Logarithm We begin by noting these facts: If a > 0 then

    Source: McGraw-Hill Professional

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