Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 81 ppt

... integration technique referred to as substitution. This will enable us to greatly expand the type of functions we can antidifferentiate. From functions h(x) and u(x) we can build the composite function ... allow us to evaluate an even broader range of definite and indefinite integrals. We will do this, using a technique called substitution, in this chapter. We can further ex...

Ngày tải lên: 05/07/2014, 18:20

... panda needs to take in C calories for every pound of the panda’s weight. i. 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. ... constants S, N, and C. ii. The number of pounds of sugar cane it takes to support a pair of pandas, one weighing P pounds and the other weighing Q pounds, for a period o...

Ngày tải lên: 05/07/2014, 18:20

... details and a very readable account, consult The History of Mathematics: An Introduction, by David Burton, McGraw-Hill Companies, Inc. 1997. 17 Due in part to their methods of record keeping and their ... climate, the ancient Egyptians and Babylonians have left modern historians more evidence of their mathematical development than have the people of other ancient civ...

Ngày tải lên: 05/07/2014, 18:20

... the graph of a famil- iar function and applying appropriate shifts, flips, and stretches. Label all x- and y-intercepts and the coordinates of any vertices and corners. Use exact values, not numerical ... average rate of change of the function g over the interval [6, 6 + h] C. The average rate of change of the function h over the interval [6, 6 + h] ii. One of the func...

Ngày tải lên: 05/07/2014, 18:20

... dollars and quantity in thousands of units. (The equilibrium occurs when supply and demand are equal.) (9, 12) 16 12 p q supply demand 4. A moving company charges a minimum of $250 for a move. An ... SLOPE OF A CURVE AND INSTANTANEOUS RATE OF CHANGE In Chapter 4 we looked at linear functions, functions characterized by a constant rate of change. This characteristic is uni...

Ngày tải lên: 05/07/2014, 18:20

... Calculating the Slope of a Curve and Instantaneous Rate of Change 183 the slope of the secant line through P and Q. By choosing Q successively closer to P , guess the slope of the tangent line at P ... Let P and Q be points on the graph of f with x-coordinates 3 and 3 + h, respectively. (a) Sketch the graph of f and the secant lines through P and Q for h = 1 and h...

Ngày tải lên: 05/07/2014, 18:20

... quantity of gas (in gallons) demanded for heating purposes, is given by q = mp + b, where m and b are constants (m negative and b positive) and p is the price of gas per gallon. The gas company ... distance. The distance between f(x )and L is |f(x)−L|. Similarly, the distance between x and3 is|x−3|. Toshow that x is within some distance δ (delta for distance) of 3 but not equal...

Ngày tải lên: 05/07/2014, 18:20

... Sketch the graph of f(t). (b) What are the domain and range of f(t)? 7.2 LEFT- AND RIGHT-HANDED LIMITS; SOMETIMES THE APPROACH IS CRITICAL ◆ EXAMPLE 7.10 How does f(x)= 1 x behave as x approaches zero? SOLUTION ... hit the value L any number of times. EXERCISE 7.2 Show, using the methods of Example 7.3, that lim x→3 k = k for any constant k. Conclude that lim x→c k = k for c an...

Ngày tải lên: 05/07/2014, 18:20

... lim x→a f(x), try values of x close to a but not too close. And then make your guess and take your chances. You’ll win some and you’ll lose some. But frequently, thoughtful graphical and numerical investigation ... =−3, x = 1, and x = 5 but doesn’t take care of the removable discon- tinuities at x =− 1and x = 0. The latter reminds us that f(a)must be defined and equal to t...

Ngày tải lên: 05/07/2014, 18:20

... a double thickness of aluminum. (a) Give an expression for the volume of the can. (b) Give an expression for the amount of material used. (Remember that the top and bottom of the can are two layers ... ? 14. A can for mandarin oranges is a cylinder with volume of 250 cubic centimeters. Denote the radius by r and the height by h. The material used for the top and bottom is...

Ngày tải lên: 05/07/2014, 18:20