Math 1a Fall 2004Final Exam Review1. Ned operates a tour service that offers the following rates:• $200 per person if 50 people (the minimum number to book the tour) go on the tour• For each additional person, up to a maximum of 80 people total, the rate per pe rson is reducedby $2.It costs $6000 (a fixed cost) plus $32 per p erson to conduct the tour. How many people does it taketo maximize Ned’s profit?2. Use Newton’s method to find the positive fourth ro ot of 2. Start with x1= 1 and find x3.3. A balloon ascending at the rate of 12 feet per second is at a height of 80 feet above the ground whena package is dropped from the balloon. How long does it take the package to reach the ground?4. Consider the definite integralZπ−π(sin x + 1) dx.(a) Estimate this integral using four approximating rectangles and right endpoints.(b) Use the Midpoint Rule with n = 5 to estimate this integral.(c) Set up an expression for this integral as a limit of Riemann sums.(d) Find the value of this integral exactly.5. Find the area of the region b e tween the x-axis and the graph of f(x) = x3− x2− 2x, −1 ≤ x ≤ 2.6. Find limx→01x3Zx0t2t4+ 1dt.7. Evaluate each of the following integrals.(a)Z√304x√x2+ 1dx(b)Z√3−√34x√x2+ 1dx(c)Z4112√y(1 +√y)2dy(d)Zsin√θrθ cos3√θdθ8. During flu season a health clinic has set up a flu shot program for its patients. The clinic is openSaturday from 8 am to 4 pm giving flu shots on a first-come, first-serve basis. The clinic has thecapacity to serve 30 patients per hour. The function r(t), whose graph is given below, gives the rateat which pe ople are arriving at the clinic for shots.9 101112 13 141516153045Express the following quantities in terms of definite integrals. For each quantity, estimate its valueusing the graph ab ove.(a) The length of the line at 11 am(b) The length of the line at its longest(c) The number of people who cam e to the clinic for flu shots(d) The number of people actually served by the c
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