Calculus the classic edition by Earl W. Swokowski

By Earl W. Swokowski

This variation of Swokowski's textual content is really as its identify implies: a vintage. Groundbreaking in each method whilst first released, this booklet is an easy, simple, direct calculus textual content. it truly is reputation is at once because of its wide use of purposes, the easy-to-understand writing sort, and the wealth of examples and routines which make stronger conceptualization of the subject material. the writer wrote this article with 3 pursuits in brain. the 1st used to be to make the ebook extra student-oriented through increasing discussions and offering extra examples and figures to assist make clear suggestions. To additional relief scholars, directions for fixing difficulties have been additional in lots of sections of the textual content. the second one goal was once to emphasize the usefulness of calculus via sleek purposes of derivatives and integrals. The 3rd target, to make the textual content as actual and error-free as attainable, used to be entire by means of a cautious exam of the exposition, mixed with a radical checking of every instance and workout.

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Note that if P(a, h) is on the graph, then the y-coordinate b is the func ti on value I(a). The figure exhibits the domain off' (the set of possible va lues of x) and the range off (the corresponding values of y), Although we have pictured the domain and range as closed intervals, they may be infinite intervals or other sets of real numbers, It is important to note that since there is exactly one value f(a) for x each a in the domain, on ly one point on the graph has x-coordinate a, I Thus. erery rerrical line intersects the graph of' a function in at most one k- Domain of J~ point.

21 n x = 4 sin 0 for - -2 < - e <- -n2 38 22 CHAPTER 1 x2 x 23 J 25 24 Jx 2 +4 25 - E xer. 45 - 54: Verify the identity. = 3 sin 0 for - ~ < 0 < ~ 2 2 x = 5 tan 0 fo r -~ < 0 < ~ 2 2 + x2 ' 9 x x 3 J x 2 - 25; 46 sec 47 csc () 2 0 = cot I + tan 2 0 48 cot 1 + ta n 1 = esc 1 sec 1 I + esc {i x= 5 sec(}fo rO < 0 < ~ 50 sec {i sin (271/ 3) (b) sin ( - 571/4) 28 (a) cos 150 (b) cos ( - 60°) 29 (a) ta n (571/ 6) (b) tan ( - 71/ 3) 30 (a) cot 120 (b) cot ( - 150 ) 31 (a) sec (271/ 3) (b) sec ( - 71/ 6) 32 (a) csc 240 0 (b) csc ( - 330) cot - f3 = cos fJ = csc z esc:: - cot z + cot :: 51 sin 3u = sin u( 3 - 4 sin 2 u) 52 2 sin 2 21 53 cos (0/ 2) = ~ 54 0 r) = I fJ - cos fJ = ta n fi sin fJ 49 - - Exer .

N (definition of y) (simplifying) Since for each x in ~ (the domain of j) the function value f(x) is in (the domain of y), the domain of 9 f is ~ . f(x)) are not always th e same; that is, I y i= 9 f. If two functions f and y both have domain ~ , then the domain of f y and y , f is also ~ . This was illustrated in Example 6. The next example shows that the domain of a composite function may differ from those of the two given functions. 0 2 2 CHAPTER I EXAMPLE 7 If {(x) = X 2 - 16 and g(x) fal (f g)(x) and the domain of { 9 0 = PRECALCULUS REVIEW Fx, find 0 fbI (g {)(x) and the domain of 9 f 0 SOLUTION We first note that the domain of f is IR and the domain of 9 is the set of all nonnegative real numbers - that is , the interval [0 , CX) ).

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