By James Stewart

Good fortune on your calculus path begins the following! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, exact, and jam-packed with proper, real-world examples. With CALCULUS, 6th variation, Stewart conveys not just the software of calculus that will help you strengthen technical competence, but additionally grants an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids may also help you construct your mathematical self belief and accomplish your ambitions within the direction!

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Extra info for Calculus: Solution Manual (5th Edition)

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T 16. (a) The sine and exponential functions have domain R , so g(t)=sin (e ) also has domain R . t t t (b) The function g(t)= 1 2 has domain {t |1 2 0}={t |2 1}={t |t 0}=(  1 x 17. Use y=Ca with the points ( 1,6 ) and ( 3,24 ) . 6=Ca 2 4=a a=2 [ since a>0 ] and C= C= 6 a 3 and 24=Ca x x 1 a= [ since a>0 ]. The function is f (x)=2 3 x+h x x h x 1 3 6 a 3 a x 2, 2 9 gives us 2 2 =2a 9  x or f (x)=2(3) . x ( h ) f (x+h) f (x) 5  5 5 5  5 5 5  1 x 19. If f (x)=5 , then = = = =5 h h h h x 24= 6 x =3 .

H 5 1 h 28 1 . 27 20. Suppose the month is February. Your payment on the 28th day would be 2 =2 =134 , 217 , 728 cents, or $1 , 342 , 177 . 28 . Clearly, the second method of payment results in a larger amount for any month. 2 24 21. 2 ft =24 in, f (24)=24 in =576 in =48 ft. g(24)=2 24 in =2 /(12 5280) mi  265 mi x 5 22. 1 ) the curves intersect. 8 until x=5 . At ( 5,3125) there is another point of intersection, and for x>5 we see that g(x)> f (x) . In fact, g increases much more rapidly than f beyond that point.

Note also that this function is even, whereas sin x is odd. 37. The graphing window is 95 pixels wide and we want to start with x=0 and end with x=2 . Since there are 94 ‘‘gaps’’ between pixels, the distance between pixels is 2  0 2 . Thus, the x  values that the calculator actually plots are x=0+ n , where 94 94 n=0 , 1 , 2 , ... , 93 , 94 . For y=sin 2x , the actual points plotted by the calculator are 2 2 sin 2 n for n=0 , 1 , ... , 94. For y=sin 96x , the points plotted 94 94 2 2 are sin 96 n for n=0 , 1 , ...

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