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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.
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Find the general solution for the follo0wing differential equation
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A gun has a muzzle speed of 100 meters per second. What angle of elevation should be used to hit an object 190 meters away? Neglect air resistance and use as the acceleration of gravity.
Determine the following quantities: fx(x, y), fy{x. y). and fxy(x, y), fxy(x, y) and fyy(x, y). Determine the equation of the tangent plane at the point (-2. 1). Use it to approximate the value of f(-1. 99, 1. 01).
bob ate 10 carrots and 7 hershey kisees and the total calories were 263. fred ate 4 carrots and 8 hershey kisses and
The movie Fatal Repulsion
write the name of congruent angles from the given figure.parallel lines bd and eg are intersected by line ah. eight
H = 4.8sin(pi/6)(t-10)+7.6, where domain of t is [0,24], and where t=0 corresponds to 12AM. When is the water level rising and falling? Find the relative extrema of H and interpret your results.
Assume that death benefits are nonincreasing. Show that the reserve at time n is higher for the starred rates (the steeper curve).
assume that for a 5-year period large-company stocks had annual rates of return of 21.54 percent -9.20 percent -11.99
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