Study Guides

Source: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill Professional 
25.
Indeterminate Forms Practice Test
Review the following concepts if needed: l’Hôpital’s Rule Help
Source: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill 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: McGrawHill Professional