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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises, find the indefinite integral and check the result by differentiation. [11² √ u³ + 2 du
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. J-8 1/3 X dx
In Exercises, find the indefinite integral and check the result by differentiation. X - x²)3 dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. S. (3√/t - 2) dt -1
In Exercises, find the indefinite integral and check the result by differentiation. EX xp (1 + x)²
In Exercises, find the indefinite integral and check the result by differentiation. x² (1 + x³)² dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. 2 X dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. X 3 √x dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. L₁ (11/3 - 12/3) di dt -1
In Exercises, find the indefinite integral and check the result by differentiation. 6x² (4x³ - 9)³ dx
In Exercises, find the indefinite integral and check the result by differentiation. x3 1 + x4 dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. fo (2 - t) √t dt
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. -8 x = x² - dx 23√x
In Exercises, find the indefinite integral and check the result by differentiation. X 1-x² dx
In Exercises, find the indefinite integral and check the result by differentiation. ¹P (³-7), (¦† + ¹ ) [
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. 0 |2x - 5| dx
In Exercises, find the indefinite integral and check the result by differentiation. 1[₁². + (3x)² dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. 4 (3 - x - 3) dx J1
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. |x² - 4x + 3| dx
In Exercises, find the indefinite integral and check the result by differentiation. 1 dx 2x
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. xp 6 - zx|
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. TT Ső (2 + cos x) dx
In Exercises, find the indefinite integral and check the result by differentiation. X /5x2 dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. m/4 0 1 - sin20 cos2 Ꮎ dᎾ
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. S™ (1 + sin x) dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. (π/6 J-π/6 sec² x dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. (π/4 sec² 0 tan² 0 + 1 de
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. *π/3 J-π/3 4 sec 0 tan 0 do
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. (π/2 π/4 (2-csc² x) dx
In Exercises evaluate the definite integral. Use a graphing utility to verify your result. (π/2 J-π/2 (2t + cos t) dt
In Exercises determine the area of the given region. y = x= x² 4 y 1 X
In Exercises determine the area of the given region. || y 2 x=
In Exercises determine the area of the given region. y = x + sin x y 4 3 2 1 I 2 R X
In Exercises determine the area of the given region. y = cos x y 1 TC 4 π X
In Exercises find the area of the region bounded by the graphs of the equations. y = x³ + x₂ x = 2, y = 0
In Exercises find the area of the region bounded by the graphs of the equations. y = 5x2 + 2, x=0, x=2, y=0
In Exercises find the area of the region bounded by the graphs of the equations. y = 1 + 3√x, x=0, x= 8, y = 0
In Exercises find the area of the region bounded by the graphs of the equations. y = 2√√√x - x, y = 0 2.
In Exercises find the value(s) of guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = √x, [4, 9]
In Exercises find the area of the region bounded by the graphs of the equations. y = -x² + 4x, y = 0
In Exercises find the area of the region bounded by the graphs of the equations. y = 1 - x4, y = 0
In Exercises find the value(s) of guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = x³, [0, 3]
In Exercises find the value(s) of guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. y 4 [0, 6]
In Exercises find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 9x², [-3,3]
In Exercises find the value(s) of guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 9 X3⁹ [1,3]
In Exercises find the value(s) of guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = 2 sec²x, TT TT 4'4
In Exercises find the value(s) of guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f(x) = cos x, TT TT 3' 3
In Exercises find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. + 1), [1,3] 4(x² + 1) x²
A function ƒ is defined below. Use12geometric formulas to find ∫012 ƒ(x) dx. f(x) = 6, 1-1/x + 9, x > 6 x≤6
A function ƒ is defined below. Usegeometric formulas to find ∫o8 ƒ(x) dx. f(x) = 4, X₂ x < 4 x ≥ 4
In Exercises find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = x³, [0, 1]
In Exercises find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = 4x³ 3x², [0, 1]
In Exercises determine which value best approximates the definite integral. Make your selection on the basis of a sketch.(a) 4(b) 4/3(c) 16(d) 2π(e) -6 JO 1/2 4 cos πx dx
In Exercises find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x)=sin x, [0, π]
In Exercises determine which value best approximates the definite integral. Make your selection on the basis of a sketch.(a) 6(b) 1/2(c) 4(d) 5/4 S 2 sin πx dx
In Exercises find the average value of the function over the given interval and all values of x in the interval for which the function equals its average value. f(x) = COS X, 0, 2
In Exercises determine which value best approximates the definite integral. Make your selection on the basis of a sketch.(a) -3(b) 9(c) 27(d) 3 xp (x^ + 1) J
The graph shows the velocity, in feet per second, of a car accelerating from rest. Use the graph to estimate the distance the car travels in 8 seconds. second) per Velocity (in
The graph shows the velocity, in feet per second, of a decelerating car after the driver applies the brakes. Use the graph to estimate how far the car travels before it comes to a stop. Velocity (in
In Exercises find possible values of a and b that make the statement true. If possible, use a graph to support your answer. (There may be more than one correct answer.) L₂ -2 5 S₁ [ 1(x) dx =
In Exercises find possible values of a and b that make the statement true. If possible, use a graph to support your answer. (There may be more than one correct answer.) 3 [ -3 + f200 f(x) dx
In Exercises find possible values of a and b that make the statement true. If possible, use a graph to support your answer. (There may be more than one correct answer.) Sº sin x dx < 0
Give an example of a function that is integrable on the interval [-1, 1], but not continuous on [-1, 1].
Let r'(t) represent the rate of growth of a dog, in pounds per year. What does r(t) represent? What does ƒ26 r'(t) dt represent about the dog?
The force F (in newtons) of a hydraulic cylinder in a press is proportional to the square of sec x, where x is the distance (in meters) that the cylinder is extended in its cycle. The domain of F is
In Exercises find possible values of a and b that make the statement true. If possible, use a graph to support your answer. So cos x dx = 0
The velocity v of the flow of blood at a distance r from the central axis of an artery of radius R iswhere K is the constant of proportionality. Find the average rate of flow of blood along a radius
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. b So [f(x) + g(x)] dx "b x = [ 1(x) dx + [ 8(x) d dx a a
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. b a f(x)g(x) dx b [[* 16x) dx][ f*^ g(x) dx] f(x)
The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model V = 0.1729t + 0.1522t² - 0.03741³, where t is the time in seconds. Approximate the
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If the norm of a partition approaches zero, then the number of
In Exercises find F of x and evaluate it at x = 2, x = 5, and x = 8. F(x) = fo 0 (4t - 7) dt
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If ƒ is increasing on [a, b], then the minimum value of ƒ(x) on
Find the Riemann sum for ƒ(x) = x² + 3x over the interval [0, 8], whereand where Xo = 0, x₁ = 1, X₂ = 3, x₂ = 7, 0 and X4 x₁ = 8
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The value ofmust be positive. b Ja f(x) dx
In Exercises find F of x and evaluate it at x = 2, x = 5, and x = 8. F(x) = x 12 (t3+2t 2) dt -
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.The value ofis 0. 2 S²² 2 sin (x²) dx
In Exercises find F of x and evaluate it at x = 2, x = 5, and x = 8. F(x) 2 = = 6₁² - 31/3d₁ dt J2
In Exercises find F of x and evaluate it at x = 2, x = 5, and x = 8. F(x) = 20 S₁3/ dv v2 1
In Exercises find F of x and evaluate it at x = 2, x = 5, and x = 8. F(x) = So sin 0 de
Find the Riemann sum for ƒ(x) = sin x over the interval [0, 2π], whereand where Xo = 0, X₁ = TT 4' X2 || 3' X3 = TT, and = 2πT,
In Exercises find F of x and evaluate it at x = 2, x = 5, and x = 8. F(x) = Si 1 cos Ꮎ dᎾ
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.Prove that x dx = b² - a² 2
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.Prove that a x² dx = b³ - a³ 3
Determine whether the Dirichlet functionis integrable on the interval [0, 1]. Explain. f(x) = 1, 0, x is rational x is irrational
Letwhere ƒ is the function whose graph is shown in the figure.(a) Estimate g(0), g(2), g(4), g(6), and g(8).(b) Find the largest open interval on which g is increasing. Find the largest open
The functionis defined on [0, 1], as shown in the figure. Show thatdoes not exist. Why doesn’t this contradict Theorem 4.4?Data from in Theorem 4.4 0, f(x) = 1 X x = 0 0 < x≤ 1
Find the constants a and b that maximize the value ofExplain your reasoning. Ja (1-x²) dx.
In Exercises (a) Integrate to find F as a function of x (b) Demonstratethe Second Fundamental Theorem of Calculus by differentiatingthe result in part (a). F(x) = f₁²a + ² (t + 2) dt
In Exercises (a) Integrate to find F as a function of x (b) Demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F(x) = Jo t(t² + 1) dt
Evaluate, if possible, the integral So 0 [x] dx.
In Exercises (a) Integrate to find F as a function of x (b) Demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F(x) = So 00 3/t dt
Determineby using an appropriate Riemann sum. lim [1² + 2² + 3² +. n→∞ n° • + n²]
In Exercises (a) Integrate to find F as a function of x (b) Demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F(x) J= J4 1/ dt
In Exercises (a) Integrate to find F as a function of x (b) Demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F(x) = TT/3 sec t tan t dt
For each continuous functionFind the maximum value of I(ƒ) - J(ƒ) over all such functions ƒ. f: [0, 1] → R, let
In Exercises use the Second Fundamental Theorem of Calculus to find F'(x). -L₁₂₁²2² F(x) = (t²- 2t) dt
In Exercises (a) Integrate to find F as a function of x (b) Demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F(x) = x π/4 sec² t dt
In Exercises use the Second Fundamental Theorem of Calculus to find F'(x). =f₁ SREI 1² + 1 F(x) = dt
In Exercises use the Second Fundamental Theorem of Calculus to find F'(x). -S₁ 0 F(x) = t cos t dt

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