By Robin J. Gottlieb

A massive grievance of professors instructing calculus is that scholars wouldn't have the perfect historical past to paintings in the course of the calculus direction effectively. this article is focused at once at this underprepared viewers. this can be a single-variable (2-semester) calculus textual content that comes with a conceptual re-introduction to key precalculus principles through the exposition as acceptable. this is often the correct source for these colleges facing poorly ready scholars or for colleges introducing a slower paced, built-in precalculus/calculus path.

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Extra info for Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition

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The number of pounds of sugar cane it takes to support a panda for a day is a function of the weight, x, of the panda. Express this function with a formula. The formula will involve the constants S, N, and C. ii. 3 Representations of Functions 27 W , the number of weeks they are to be supported. Express this function as a formula. The formula will involve the constants S, N, C, P , and Q. SOLUTION i. Let’s use the strategy of taking the problem apart into a series of simpler questions. We’ll use unit analysis to help us.

Instead, we must draw a triangle that involves the radius of the bowl itself. This radius must emanate from the center of the sphere. 11 4h − h2. ◆ Functioning with friends. Javier goes to a pizza shop intending to order a small pizza and eat it. When he enters the shop he sees some of his friends and they decide to split a large pizza. If the radius of a large pizza is twice the radius of a small pizza, what fraction of the large pizza should be allocated to Javier to give him the amount of food he originally intended to eat?

A) C(A) (b) C(2A) (c) 2C(A) (d) C(A + 1) (e) C(A) + 1 1 x+1 , 14. If f (x) = find the following. Simplify your answer where possible. (a) f (0) (b) f (3) (f ) f (b + 3) 15. If g(x) = (a) g(0) 16. If h(x) = (a) h(0) (g) [f (7)]2 (c) f (− 41 ) (h) (d) f (b) f (b2) (i) [f (b)]2 (e) f (b − 1) √ x 2 +4 , 2 find the following. Simplify your answer where possible. √ √ (e) −g(3t) (f ) g( t − 4) (b) g(2) (c) g( 5) (d) g √1 2 x2 1−2x , find (b) h(3) (c) h(p + 1) (d) h(3p) (e) 2h(3p) (f ) 1 h(2p) 17. If j (x) = 3x 2 − 2x + 1, find the following.