TAILIEUCHUNG - Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 76

Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 76. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | The Definite Integral Qualitative Analysis and Signed Area 731 a The lead the chicken has when the goat begins to move b The distance between the goat and the chicken at time t c The distance between the goat and the chicken at time t 3 d The time at which the goat is farthest ahead of the chicken e Approximate the time s at which the chicken and the goat pass one another on the path. f Approximate the time at which the distance between the goat and the chicken is increasing most rapidly. At this time what is the relationship between v g and v c 6. Suppose we want to approximate 02 x dx by partitioning the interval 0 2 into n equal pieces and constructing left- and right-hand sums. Let x x3. a Put the following expressions in ascending order. x dx 4 R4 L20 R20 100 R100 0 b Find R4 - 4I. c Find IR100 - 1001. d How large must n be to assure that Rn - n e Write out R4 once using summation notation once without. Evaluate R4. 7. Turn back to Problem 1 ofProblems for Section on page 723. Express the following quantities using a definite integral or the sum or difference of definite integrals. a The length of the line at 11 00 . b The length of the line at its longest c The number of people who came to the clinic for flu shots d The number of people actually served by the clinic e The length of the line at 3 00 . f The amount of time a person arriving at noon has to wait in line g The amount of time by which the clinic must extend its hours in order to serve everyone who is in line before 4 00 . 8. Repeat parts a through e of Problem 6 letting x xpr- THE DEFINITE INTEGRAL QUALITATIVE ANALYSIS AND SIGNED AREA In Section we established that the signed area under a rate graph is of particular interest to us this area corresponds to the net change in amount. In Section we established that if is a reasonably well-behaved function 10 we can in theory find the signed area under the graph of t on the interval a as follows. Partition the

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