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New PDF release: Calculus I (Undergraduate Texts in Mathematics)

By Jerrold Marsden, Alan Weinstein

ISBN-10: 0387909745

ISBN-13: 9780387909745

Undergraduate Texts in arithmetic

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Additional resources for Calculus I (Undergraduate Texts in Mathematics)

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Passes through ( - I , - 1); slope = - 10 43. Find the coordinates of the point which is a distance 3 from the x axis and a distance 5 from (1>2). ir44. (a) Find the coordinates of a point whose distance from (0,O) is 2 p and whose distance from (4,4) is 2 n . (b) If h > 2Q show both algebraically and geometrically that there are exactly two points whose distance from (0,O) is h and whose distance from (4,4) is also A. 5 Circles and Parabolas (x - a)' + ( y - b)* = r2 is a circle and y = a(x - p)' + q is a parabola.

B)(b . . b ) nrn times = b"". - and (bc)"= bcbc . . bc = ( b . . b ) ( c . . c ) r y n times n times n times = bncn. Example 1 Solution Simplify (a) 2". 5" (b) (a) 2'' . 5'' = (2 . 2)1° + 39 39 10". The first of the three laws of exponents is particularly important; it is the basis for extending the operation of exponentiation to allow negative exponents. If b0 were defined, we ought to have bobn= bO+"= bn. If b # 0, then b n f 0, and the equation bobn= b n implies that b0 must be 1. We take this as the definition of bO,noting that 0' is not defined (see Exercise 31).

Can inter- 2, 3, or 4 Copyright 1985 Springer-Verlag. All rights reserved. Chapter 1 Derivatives and Limits Differentiation is one of the two fundamental operations of calculus.

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Calculus I (Undergraduate Texts in Mathematics) by Jerrold Marsden, Alan Weinstein


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