The following sections of this BookRags Literature Study Guide is offprint from Gale's For Students Series: Presenting Analysis, Context, and Criticism on Commonly Studied Works: Introduction, Author Biography, Plot Summary, Characters, Themes, Style, Historical Context, Critical Overview, Criticism and Critical Essays, Media Adaptations, Topics for Further Study, Compare & Contrast, What Do I Read Next?, For Further Study, and Sources.
(c)1998-2002; (c)2002 by Gale. Gale is an imprint of The Gale Group, Inc., a division of Thomson Learning, Inc. Gale and Design and Thomson Learning are trademarks used herein under license.
The following sections, if they exist, are offprint from Beacham's Encyclopedia of Popular Fiction: "Social Concerns", "Thematic Overview", "Techniques", "Literary Precedents", "Key Questions", "Related Titles", "Adaptations", "Related Web Sites". (c)1994-2005, by Walton Beacham.
The following sections, if they exist, are offprint from Beacham's Guide to Literature for Young Adults: "About the Author", "Overview", "Setting", "Literary Qualities", "Social Sensitivity", "Topics for Discussion", "Ideas for Reports and Papers". (c)1994-2005, by Walton Beacham.
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Indeterminate limits are mathematical expressions that cannot be assigned a unique value. Although these expressions have no meaning per se, they frequently arise in limit problems in calculus. For example, to compute the derivative (slope) of the sine curve at any point on the curve, one needs to evaluate the limit of sin(x)/x as x approaches 0. Simple substitution of x = 0 into this expression does not produce a satisfactory result: It gives the indeterminate limit 0/0. But a more careful approach, using the "sandwich principle" of calculus, shows that the correct value of the limit is actually 1.
Generally speaking, a limit of a quotient of two functions, f(x)/ g(x), is said to be indeterminate of the form 0/0 if both f(x) and g(x) approach 0. The actual limit of f(x)/ g(x) in such a case depends on more detailed information about these two functions - intuitively, which one approaches 0 "faster." A powerful tool for evaluating such limits is L'Hospital's Rule, which provides the needed information by comparing the derivatives of f(x) and g(x).
Besides 0/0, the other commonly occurring indeterminate limits are (infinity)/(infinity), (infinity) - (infinity), 1(infinity), (infinity)0, and 00. L'Hospital's Rule applies directly to the first of these; the other four generally need to be transformed algebraically before l'Hospital's Rule can be applied.