By James Stewart
Good fortune on your calculus path begins right here! James Stewart's CALCULUS texts are world-wide best-sellers for a cause: they're transparent, actual, and jam-packed with correct, real-world examples. With CALCULUS: EARLY TRANCENDENTALS, 6th variation, Stewart conveys not just the software of calculus that will help you strengthen technical competence, but additionally promises an appreciation for the intrinsic fantastic thing about the topic. His sufferer examples and integrated studying aids can help you construct your mathematical self belief and attain your targets within the direction!
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Additional info for Calculus: Early Transcendentals (6th Edition) (Stewart's Calculus Series)
Express the area of the rect- angle as a function of the length of one of its sides. 1 FOUR WAYS TO REPRESENT A FUNCTION 52. A rectangle has area 16 m2. Express the perimeter of the rect- |||| 23 (b) How much tax is assessed on an income of $14,000? On $26,000? (c) Sketch the graph of the total assessed tax T as a function of the income I. angle as a function of the length of one of its sides. 53. Express the area of an equilateral triangle as a function of the length of a side. 54. Express the surface area of a cube as a function of its volume.
Draw a rough graph of T as a function of the time t that has elapsed since the faucet was turned on. T SOLUTION The initial temperature of the running water is close to room temperature t 0 FIGURE 11 because the water has been sitting in the pipes. When the water from the hot-water tank starts flowing from the faucet, T increases quickly. In the next phase, T is constant at the temperature of the heated water in the tank. When the tank is drained, T decreases to the temperature of the water supply.
If we plot these values, we get the graph (called a scatter plot) in Figure 9. It too is a useful representation; the graph allows us to absorb all the data at once. What about a formula? Of course, it’s impossible to devise an explicit formula that gives the exact human population P͑t͒ at any time t. But it is possible to find an expression for a function that approximates P͑t͒. ” The function f is called a mathematical model for population growth. In other words, it is a function with an explicit formula that approximates the behavior of our given function.