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Definite Integrals-
Exercise 1- Express the limit limn→∞ i=1Σn xi ln(1 + xi2)?x, where ?x = 6-2/n and xi = 2 + i?x, as a definite integral on the interval [2, 6].
Exercise 2- Compute 0∫2(2x - x3)dx.
Exercise 3- Compute 0∫4exdx.
Exercise 4- Prove that a∫bx dx = 1/2 (b2 - a2). Note that this is f(b) - f(a) where f(x) = ½ x2.
Exercise 5- Prove that a∫bx2 dx = 1/3(b3 - a3). Note that this is f(b) - f(a) where f(x) = 1/3 x3.
Exercise 6- Express the integral 1∫10(x - 4 ln x) dx as a limit of Riemann sums as in (1).
Exercise 7- Use the properties of integrals (page 379 to 381) to verify the following inequality without evaluating an integral:
2 ≤ -1∫1√(1 + x2) dx ≤ 2√2.
a right circular cone of height 3 and radius (at the base) equal to 8. What are the dimensions of such a cylinder which has maximum volume?
A plane flying horizontally at an altitude of 3 mi and a speed of 420 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station.
Find a polar equation to describe curve represented by Cartesian equation 3x^2+3y^2=16
A ball is thrown upward at a speed of 17 ft/s from the top of a 188 foot high building. What is the maximum height of the ball? Round your answer to the nearest hundredth of a foot.
Estimate the volume V of the mound by computing the average of the two Riemann sums4,3 with lower-left and upper-right vertices of the sub rectangles as sample points.
A nutrition laboratory tests 50 "reduced sodium" hot dogs, finding that the mean sodium content is 316 mg, with a standard deviation of 35 mg.
Two angles of a triangle measure 15 degrees and 85 degrees. What is the measure for the third angle?
Examine specific approaches that a negotiator could take to reduce the chances of an escalation before reaching a final decision in the negotiation process.
a nutrition label for oriental spice states that one package of the sauce has 1190 milligrams of sodium. to determine
Using the tables, find the Laplace Transforms: (a) f(t) = 2 -t^3/6+ cos(2t) - e^(3t)
The hypotenuse of a right triangle is 10 ft longer than the shortest side. If the sum of the lengths of the two legs is 35 ft, find the lengths of all three sides.
The following parametric equations trace out a loop. Find the t values at which the curve intersects itself. Find the x and y values of the intersection.
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