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1. Show that -∞∫∞ (1 + x) / (1 + x2) dx diverges, but limt→∞-t∫t (1 + x) / (1 + x2) dx = π.
2. Use the Comparison Theorem to decide if these integrals converge or diverge.
a. 1∫∞ (4 + e-x) / x dxb. 0∫∞ arctan x / (2 + ex) dx
3. The Gamma function is defined by Γ(t) = 0∫∞ xt-1 e-x dx. Use integration by parts to prove that Γ(z + 1) = z Γ(z).
4. Consider the curve y = 1/x for x ≥ 1.
a. Show that the area under the curve is infinite.
b. Show that the volume of the solid of revolution enclosed by the curve is finite, and compute it. [This solid of revolution is known as Gabriel's Horn.]
Estimate all the stationary points
Discuss examples of administrative decisions that might be made in the managing of performance of professor?
A chandelier was marked up 150% from an original cost of $96. Last Friday, Tamir bought the chandelier and paid an additional 5% in sales tax. What was his total cost
A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that the population standard deviation of the lifetime is 500 hours. Construct a 95% confidence interval estimate of the mean lifetime
Find the midpoint and length of the line segment PQ where P=(2,-7) and Q=(5,1). We will also use vectors to find the length of the segment.
A plane flying horizontally at an altitude of 1 mi and a speed of 440 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.
A simple pulley with the given radius used to lift heavy objects is positioned 10 feet above ground level. Given that the pulley rotates theta degrees, determine the height to which the object is lifted. a) r=4 in, theta=720 degrees b) r=2 ft, the..
What is the probability of getting the indicated result
Interpreting political Polling: A pollster surveys 200 people and asks them their preference of political party. He codes the responce as 0 1 2 3. He then calculates the average of the numbers and gets 0.95. How can that value be interpreted.
A student in this class wants an A for the course. The quiz average was 88%. The score for each presentation and for the project was 90%. The exam 1 grade was 92% and the exam 2 grade was 94%. A boost of 4% has been earned. What grade on the ..
throughout the 1990s the average household expenditure on scratch tickets in a state has been 5. in 2010 a sample of 7
Malik popped a ball straight up with an initial upward velocity of 45 feet per second. The hight h, in feet, of the ball above the ground is modeled by the equation h=2+48t-16t2. How long was the ball in the air if the catcher catches the ball whe..
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