Study Guides
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41.
The Area Between Two Curves Help
Introduction to The Area Between Two Curves Frequently it is useful to find the area between two curves. See Fig. 4.17. Following the model that we have set up earlier, we first note that the intersected region has left endpoint at x = a ...
Source: McGraw-Hill Professional -
42.
Rules of Integration Help
Rules of Integration We have been using various rules of integration without enunciating them explicitly. It is well to have them recorded for future reference. Linear Properties
Source: McGraw-Hill Professional -
Source: McGraw-Hill Professional
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Source: McGraw-Hill Professional
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45.
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 -
46.
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 to be ...
Source: McGraw-Hill Professional -
47.
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 -
48.
Indeterminate Forms Practice Test
Review the following concepts if needed: l’Hôpital’s Rule Help
Source: McGraw-Hill Professional -
49.
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 -
50.
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
