By James Stewart, Daniel Clegg

New from James Stewart and Daniel Clegg, short utilized CALCULUS takes an intuitive, much less formal method of calculus with no sacrificing the mathematical integrity. that includes quite a lot of purposes designed to encourage scholars with various pursuits, transparent examples detailing vital mathematical tactics, and an enormous selection of workouts acceptable for college students with disparate ability units, this primary version is ideal for college kids who have to easy methods to observe calculus recommendations instead of reflect the formal proofs in the back of the ideas. Early assurance of exponential and logarithmic capabilities permits the inclusion of many fascinating purposes through the textual content. to be had with quite a number vitamins together with more desirable WebAssign, short utilized CALCULUS makes calculus approachable so any pupil can comprehend the suggestions and be triumphant within the path.

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A) If a second reservoir’s water depth is given by t͑t͒ f ͑t͒ Ϫ 15, how do the water levels of the two reservoirs compare? (b) What if the second reservoir’s depth is t͑t͒ f ͑t Ϫ 2͒? (c) What if the second reservoir’s depth is t͑t͒ f ͑t ϩ 2͒? 8 f ͑t͒? 37. The graph of f is given. Use it to graph the following functions. (a) y f ͑2x͒ (b) y f ( 12 x) (d) y Ϫf ͑Ϫx͒ y 1 0 x 1 38– 42 ■ The graph of y sx is shown in Figure 8(a). Use transformations to graph each of the following functions.

If p͑x͒ sx ϩ 1 and q͑x͒ 2x Ϫ 4, write a formula for each of the following functions. What is the domain? (a) A͑x͒ p͑x͒ ϩ q͑x͒ (b) B͑x͒ p͑x͒ Ϫ q͑x͒ (c) C͑x͒ p͑x͒ q͑x͒ (d) D͑x͒ p͑x͒͞q͑x͒ 11. If f ͑x͒ x 2 ϩ 1, t͑t͒ 4t Ϫ 2, A͑t͒ f ͑t͑t͒͒, and B͑x͒ t͑ f ͑x͒͒, compute A͑3͒ and B͑3͒. 12. If h͑n͒ 2 Ϫ 5n, p͑n͒ n 2 Ϫ 3, u͑n͒ h͑ p͑n͒͒, and v͑n͒ p͑h͑n͒͒, compute u͑2͒ and v͑2͒. 13. If M͑t͒ t ϩ st , N͑t͒ 3t ϩ 7, C͑t͒ M͑N͑t͒͒, and D͑t͒ N͑M͑t͒͒, compute C͑3͒ and D͑4͒. 14. If f ͑t͒ t 3 ϩ 2, t͑x͒ 2x ϩ 3, p͑x͒ f ͑t͑x͒͒, and r͑t͒ t͑ f ͑t͒͒, compute p͑Ϫ1͒ and r͑Ϫ2͒.

The rule that connects s and A is given by the equation A s 2. With each positive number s there is associated one value of A, and we can say that A is a function of s. B. The human population of the world P depends on the time t. The table gives estimates of the world population for certain years. For instance, when t 1950, P Ϸ 2,560,000,000. But for each value of the time t there is a corresponding value of P, and we say that P is a function of t. C. The cost C of mailing an envelope depends on its weight w.