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mathematics
college mathematics for business economics

Questions and Answers of College Mathematics For Business Economics

In Problems 9–24, find each indefinite integral. Check by differentiating. Z dz
In Problems 9–44, find each indefinite integral and check the result by differentiating. Jo (x + 3) ¹⁰ dx
In Problems 9–24, find each indefinite integral. Check by differentiating. Z dz
In Problems 9–44, find each indefinite integral and check the result by differentiating. f (x − 3)-4 dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. Jo (6t - 7)-² dt
In Problems 9–24, find each indefinite integral. Check by differentiating. [se 5e" du
Is F(x) = (x + 1) (x + 2) an antiderivative of f(x) = 2x + 3? Explain.
Is F(x) = (2x + 5) (x - 6) an antiderivative of f(x) = 4x − 7? Explain.
In Problems 9–44, find each indefinite integral and check the result by differentiating. (1³ + 4)-² 1² dt
Is F(x) = 1 + x ln x an antiderivative of f(x) = 1 + ln x? Explain.
In Problems 9–44, find each indefinite integral and check the result by differentiating. ter² xe dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. Jea е -0.01x dx
Is F(x) = x ln x - x + e an antiderivative of f(x) = ln x? Explain.
In Problems 9–44, find each indefinite integral and check the result by differentiating. X 1 + x² dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. S X 1 + x² 5dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. el-i -t dt
In Problems 9–44, find each indefinite integral and check the result by differentiating. 3 √2³. -dt t
In Problems 9–44, find each indefinite integral and check the result by differentiating. f 2 (31² + 1)4 dt
In Problems 33-38, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The constant function f(x) = π is an antiderivative of the
In Problems 33-38, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The constant function k(x) = 0 is an antiderivative of the
In Problems 9–44, find each indefinite integral and check the result by differentiating. 1² ( 1³ - 2) 5 S dt
In Problems 33-38, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The constant function k(x) itself. = O is an antiderivative of
In Problems 33-38, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.If n is an integer, then x + 1/ (n + 1) is an antiderivative of
In Problems 9–44, find each indefinite integral and check the result by differentiating. fxVx- x - 9 dx
In Problems 33-38, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample.The function h(x) = 5ex is an antiderivative of it self.
In Problems 9–44, find each indefinite integral and check the result by differentiating. X Vx - 3 dx
In Problems 33-38, discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. The constant function g(x) itself. 5e is an antiderivative of
In Problems 9–44, find each indefinite integral and check the result by differentiating. S X Vx+ 5 dx
In Problems 39-42, could the three graphs in each figure be anti- derivatives of the same function? Explain. -4 0 4 x
In Problems 9–44, find each indefinite integral and check the result by differentiating. [x(x-4)º dx
In Problems 39-42, could the three graphs in each figure be anti- derivatives of the same function? Explain. -4 X
In Problems 9–44, find each indefinite integral and check the result by differentiating. [x(x x(x + 6)³ dx
In Problems 39-42, could the three graphs in each figure be anti- derivatives of the same function? Explain. 4
In Problems 9–44, find each indefinite integral and check the result by differentiating. √₁² (1+ (1 + e²x)³ dx
In Problems 39-42, could the three graphs in each figure be anti- derivatives of the same function? Explain. 4 4 0 X
In Problems 9–44, find each indefinite integral and check the result by differentiating. [₁³ (1- ex (1 –ex) 4 dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. 1 + x 4 + 2x + x² 2 -dx
In Problems 9–44, find each indefinite integral and check the result by differentiating. 43 1²-1 -dx - 3x + 7
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that
In Problems 45–50, the indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Then find it without using substitution. Check that
Is F(x) = x2ex an antiderivative of f(x) = 2xex? Explain.
Is F(x) = 1/x an antiderivative of f(x) X = In x? Explain.
Is F(x) = (x2 + 4)6 an antiderivative of f(x) = 12x(x2 + 4)5? Explain.
In Problems 55-62, find the particular antiderivative of each derivative that satisfies the given condition. C'(x) = 6x²4x; C(0) = 3,000
In Problems 55-62, find the particular antiderivative of each derivative that satisfies the given condition. R'(x) = 600 0.6x; R (0) = 0 -
In Problems 55-62, find the particular antiderivative of each derivative that satisfies the given condition. dx dt || 20 √x(1) = 40
In Problems 55-62, find the particular antiderivative of each derivative that satisfies the given condition. dR dt || 100 2 ;R(1) = 400
In Problems 55-62, find the particular antiderivative of each derivative that satisfies the given condition. dy dx 2x² + 3x¹1; y(1) = 0
In Problems 59–70, find each indefinite integral and check the result by differentiating. [x√3x x√3x² + 7 dx
In Problems 55-62, find the particular antiderivative of each derivative that satisfies the given condition. dy dx = 3x¹ + x²²; y(1) = 1
In Problems 55–62, find the particular antiderivative of each derivative that satisfies the given condition. dx dt =4e¹ 2; x(0) = 1 -
In Problems 59–70, find each indefinite integral and check the result by differentiating. √x(x³ x(x² + 2)² dx
In Problems 55–62, find the particular antiderivative of each derivative that satisfies the given condition. dy dt 5e¹4; y(0) −1 -1
In Problems 59–70, find each indefinite integral and check the result by differentiating. xp z ( T + zx ) x
In Problems 59–70, find each indefinite integral and check the result by differentiating. [x²(2³ x²(x³ + 2)² dx
In Problems 59–70, find each indefinite integral and check the result by differentiating. [a (x² + 2)² dx
In Problems 59–70, find each indefinite integral and check the result by differentiating. +3 √2x² + 3 dx
In Problems 65–70, find each indefinite integral. 2x4 to X dx
In Problems 59–70, find each indefinite integral and check the result by differentiating. +² =dx √4x³ - 1
In Problems 59–70, find each indefinite integral and check the result by differentiating. S (In x) X - dx
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function.f(x) = -x2 + 2x + 4
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).f(x) = ln(x2 + 4)
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = X ²-4
Find each limit in Problems 31–40. X [ — x () —x lim
In Problems 27-32, find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. _f(x) = |x|
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function.f(x) = x3 + x
In Problems 31-40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. f(x) = x²
In Problems 31-40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. f(x) = x²
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 1 x² - 4
Find each limit in Problems 31–40. x²-3x - 4 5x+4 lim x-4x²
In Problems 27-32, find (A) f'(x), (B) the partition numbers for f', and (C) the critical numbers of f. f(x) = |x + 3|
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function.f(x) = -x3 - 2x
In Problems 31–40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. f(x) =
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 1 1 + x²
Find each limit in Problems 31–40. lim x-0 In(1+x) 2
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function.f(x) = 8x3 - 2x4
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) x² 1 + x²
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.f(x) = 2x2 - 4x
In Problems 31–40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points.
Find each limit in Problems 31–40. In (1 + x) lim x 0 1 + x
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 2x 1-x²
In Problems 31–40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. f(x) =
Find each limit in Problems 31–40. 4x e lim X x²
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) = x + 16 | X
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = 2.x ²-9
Find each limit in Problems 31–40. 1³ x0e-x-1 et lim
In Problems 31–40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. f(x)
In Problems 33–36, explain why L’Hôpital’s rule does not apply. If the limit exists, find it by other means. lim x-3 1² (x + 3) 5
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) = x + 25
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) = -5x (x - 1)²
Find each limit in Problems 31–40. lim x-0¹ V1 + x - 1 Vx
In Problems 31–40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. f(x) = ln
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x 0 4x -
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) = x² x² + 1 X
In Problems 33-46, find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema. 8 + x x = (x)ƒ
In Problems 19–58, summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x). f(x) X (x - 2)²
In Problems 31–40, find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. (EI + x9
Find each limit in Problems 37–60. Note that L’Hôpital’s rule does not apply to every problem, and some problems will require more than one application of L’Hôpital’s rule. lim x-0 3x +
In Problems 27–42, find the absolute maximum and minimum, if either exists, for each function. f(x) 1 x² + 1

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