By James Stewart
This top promoting writer crew explains ideas easily and obviously, with no glossing over tricky issues. challenge fixing and mathematical modeling are brought early and bolstered all through, in order that whilst scholars end the direction, they've got a high-quality beginning within the ideas of mathematical considering. This complete, calmly paced booklet offers whole assurance of the functionality proposal and integrates sizeable graphing calculator fabrics that support scholars strengthen perception into mathematical rules. The authors' realization to aspect and readability, as in James Stewart's market-leading Calculus textual content, is what makes this article the marketplace chief.
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Additional resources for Precalculus: Mathematics for Calculus, 5th Edition, Enhanced WebAssign Edition
Sample text
What happens to the nth root of n as n gets large? Discovery • Discussion 98. How Big Is a Billion? If you have a million (106) dollars in a suitcase, and you spend a thousand (10 3) dollars each day, how many years would it take you to use all the money? Spending at the same rate, how many years would it take you to empty a suitcase filled with a billion (10 9 ) dollars? 3 n 101. Comparing Roots Without using a calculator, determine which number is larger in each pair. (a) 21/2 or 21/3 (b) A 12 B 1/2 or A 12 B 1/3 (c) 71/4 or 41/3 3 (d) 1 5 or 13 Algebraic Expressions A variable is a letter that can represent any number from a given set of numbers.
In other Mathematics in the Modern World, we will describe in more detail how mathematics affects all of us in our everyday activities. Example 5 Simplifying Expressions with Negative Exponents Eliminate negative exponents and simplify each expression. y Ϫ2 6st Ϫ4 (a) (b) a 3 b Ϫ2 2 2s t 3z Solution (a) We use Law 7, which allows us to move a number raised to a power from the numerator to the denominator (or vice versa) by changing the sign of the exponent. tϪ4 moves to denominator and becomes t4.
A y Ϫ2 3z 3 2 b b ϭ a y 3z 3 ϭ 9z 6 y2 Law 6 Laws 5 and 4 ■ Scientific Notation Exponential notation is used by scientists as a compact way of writing very large numbers and very small numbers. For example, the nearest star beyond the sun, Proxima Centauri, is approximately 40,000,000,000,000 km away. 00000000000000000000000166 g. Such numbers are difficult to read and to write, so scientists usually express them in scientific notation. Scientific Notation A positive number x is said to be written in scientific notation if it is expressed as follows: x ϭ a ϫ 10n where 1 Յ a Ͻ 10 and n is an integer For instance, when we state that the distance to the star Proxima Centauri is 4 ϫ 1013 km, the positive exponent 13 indicates that the decimal point should be moved 13 places to the right: 4 ϫ 1013 ϭ 40,000,000,000,000 Move decimal point 13 places to the right.