By Serge Lang
This 5th version of Lang's publication covers the entire subject matters typically taught within the first-year calculus series. Divided into 5 components, every one part of a primary direction IN CALCULUS comprises examples and purposes in relation to the subject coated. additionally, the rear of the ebook includes certain ideas to a lot of the routines, letting them be used as worked-out examples -- one of many major advancements over earlier variations.
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This 5th variation of Lang's publication covers the entire issues routinely taught within the first-year calculus series. Divided into 5 components, every one portion of a primary direction IN CALCULUS includes examples and functions when it comes to the subject coated. additionally, the rear of the ebook comprises distinct ideas to lots of the routines, letting them be used as worked-out examples -- one of many major advancements over earlier variants.
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Additional info for A First Course in Calculus, 3rd Edition
Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. ■ 12 Chapter 0 ■ Fundamental Concepts of Algebra Basic Rules of Algebra The four basic arithmetic operations are addition, multiplication, subtraction, and division, denoted by the symbols ϩ, ϫ or и , Ϫ, and Ϭ, respectively. Of these, addition and multiplication are considered to be the two primary arithmetic operations.
Simplify. 12a3bϪ4 12a3 и a2 ϭ 4aϪ2b 4b и b4 3a5 ϭ 5 b 2 Ϫ2 d. Rewriting with Positive Exponents 3xy 3Ϫ2͑x2͒Ϫ2 yϪ2 3Ϫ2xϪ4 ϭ Ϫ2 y ϭ y2 32x 4 y2 ϭ 4 9x ϭ Definition of negative exponent Product of Powers Property Power of a Quotient and Power of a Product Properties Power of a Power Property Definition of negative exponent Simplify. Checkpoint 2 Rewrite r = 2 ft Ϫ3 x z 3 Ϫ2 4 with positive exponents and simplify. Example 3 ■ Ratio of Volume to Surface Area The volume V and surface area S of a sphere are given by 4 V ϭ r3 and 3 S ϭ 4 r2 where r is the radius of the sphere.
2 ■ The Basic Rules of Algebra 13 Because subtraction is defined as “adding the opposite,” the Distributive Property is also true for subtraction. For instance, the “subtraction form” of a͑b ϩ c͒ ϭ ab ϩ ac is a͑b Ϫ c͒ ϭ a ͓ b ϩ ͑Ϫc͔͒ ϭ ab ϩ a͑Ϫc͒ ϭ ab Ϫ ac. Example 4 Identifying the Basic Rules of Algebra Identify the rule of algebra illustrated by each statement. a. ͑4x2͒5 ϭ 5͑4x2͒ b. ͑2y3 ϩ y͒ Ϫ ͑2y3 ϩ y͒ ϭ 0 c. ͑4 ϩ x2͒ ϩ 3x2 ϭ 4 ϩ ͑x2 ϩ 3x2͒ d. ͑x Ϫ 5͒7 ϩ ͑x Ϫ 5͒x ϭ ͑x Ϫ 5͒͑7 ϩ x͒ e. 2x и 1 ϭ 1, 2x x 0 SOLUTION STUDY TIP Note that in Example 4(e), it is important that x be a nonzero number.
A First Course in Calculus, 3rd Edition by Serge Lang