Problems 39–66 are mixed—some may require use of the integration -by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g ( x ) > 0 whenever ln g ( x ) is involved. 43. ∫ 1 e ln x x 2 d x
Problems 39–66 are mixed—some may require use of the integration -by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g ( x ) > 0 whenever ln g ( x ) is involved. 43. ∫ 1 e ln x x 2 d x
Solution Summary: The author explains how to obtain the value of v by integrating the equation dv=1x2.
Problems 39–66 are mixed—some may require use of the integration-by-parts formula along with techniques we have considered earlier; others may require repeated use of the integration-by-parts formula. Assume that g (x) > 0 whenever ln g(x) is involved.
43.
∫
1
e
ln
x
x
2
d
x
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
iid
B1 Suppose X1, ..., Xn
fx(x), where
2
fx(x) = x exp(−x²/0),
0<< (0 otherwise).
(a) Find the maximum likelihood estimator of 0.
(b) Show that the MLE is an unbiased estimator of 0.
(c) Find the MSE of the MLE.
Hint: For parts (b) and (c), you may use integration by parts.
4. Suppose the demand for a certain item is given by D(p)=-2 p² - 4p+350, where p represents the price of
the item in dollars.
a) Find the rate of change of demand with respect to price.
b) Find and interpret the rate of change of demand when the price is $11.
√3-x, x≤3,
2. For f(x) =
1
find each of the following.
x > 3,
x-3'
1. f(-6)
2. f(3)
3. f(7)
3. Find the domain of each of the following functions.
Chapter 6 Solutions
MyLab Math with Pearson eText - Stand Alone Access Card - for Calculus for Business, Economics, Life Sciences & Social Sciences, Brief Version (14th Edition)
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