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mathematics
calculus 10th edition

Questions and Answers of Calculus 10th Edition

In Exercises find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.y = 4 + 2x - x², y = 4 - x(a) The x-axis(b) The line y = 1
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis. x = - y² + 4y y 4 3 2 1 1 2 3 نرا 4 X
In Exercises find the arc length of the graph of the function over the indicated interval. y = ln(sin x), З п 4' 4 Fit
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = 4x - x², x = 0, x = 0, y = 4
In Exercises find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.(a) The x-axis(b) The y-axis(c) The line x = 3(d) The line x
In Exercises find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines.y = x², y = 4x - x²(a) The x-axis(b) The line y = 6
In Exercises find the arc length of the graph of the function over the indicated interval. y 3 x2/3 x2/3 + 4, [1,27]
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x³/2, y = 8, x = 0
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y=9x², y = 0
In Exercises find the volumes of the solids generated by revolving the region bounded by the graphs of the equations about the given lines. y = 2x², y = 0, x = 2(a) The y-axis(b) The x-axis(c)
In Exercises find the arc length of the graph of the function over the indicated interval. y x² 1 6х3 + 10 [2,5]
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis. y = x²/3 1 y 1 -X
In Exercises find the arc length of the graph of the function over the indicated interval. y || 100 + 1 4x²³ [1, 3]
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis. y =√16x² 4 3 2 y 1 2 +3 3 4 X
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x², y = 4x - x²
In Exercises find the arc length of the graph of the function over the indicated interval. y = x²/3,[1,8]
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the y-axis. y = x² y 4 3 2 1 1 2 + + 3 4 X
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = 1/r³₁ 2x³, y = 0, y = 0, x =
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y = 2, y = 4- -3 -2 -1 y 5 st 3 نرا 1 x² 4 H 2 3 X
In Exercises find the arc length of the graph of the function over the indicated interval. y = 2x³/2 + 3 60 50 40 30 20 10 H y=2x3/2+3] 2 4 6 8 10 12
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y = x², y = x² 1 1 J+x X
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y ==x², y = 0, x = 4
In Exercises find the arc length of the graph of the function over the indicated interval. y -1 = 4 3 2 1 نرا -1 -x3/2 + 1 y = ²x³/2+1 2 3 نرا 4
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = √√√x 4 2 x^ y 2 4 X
In Exercises find the arc length of the graph of the function over the indicated interval. y 4 3 2 || 6 + + 1 1 2x 2 y: + 3 6 + 4 1 2x
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y = √x 4 3 نرا 2 1 1 2 3 4 X
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y = √√√9-x² 3 2 1 2 3 X
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = 1 - x y 1 X
In Exercises find the arc length of the graph of the function over the indicated interval. - = 4 3 2 1 1 -1 (x² + 1)3/2 y |y=(x²+1)3/2 1 2 3 4
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y = 4x² 4 3 2 1 1 12 3 4 X
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. y = x 2 1 y 1 2 X
In Exercises set up and evaluate the integral that gives the volume of the solid formed by revolving the region about the x-axis. y = -x + 1 y 1 -X
In Exercises find the distance between the points using (a) The Distance Formula (b) Integration(1, 2), (7, 10)
In Exercises find the distance between the points using (a) The Distance Formula (b) Integration(0, 0), (8, 15)
In Exercises solve the Bernoulli differential equation. The Bernoulli equation is a well-known nonlinear equation of the formthat can be reduced to a linear form by a substitution. The general
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 graphs of ƒ and g intersect midway between x = a and x =
The horizontal line y = c intersects the curve y = 2x - 3x³ in the first quadrant as shown in the figure. Find c so that the areas of the two shaded regions are equal. y y=c y=2x-3x³ X
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 linedivides the region under the curveon [0, 1] into two
Find the area between the graph of y = sin x and the line segment joining the points (0, 0) and as shown in the figure. 7 п 6 −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.Ifthen la [f(x) = g(x)] dx = A -
Let a > 0 and b > 0. Show that the area of the ellipseis πab (see figure). X D ** b 1
The surface of a machine part is the region between the graphs of y1 = |x| and y₂ = 0.08x² + k (see figure).(a) Find k where the parabola is tangent to the graph of y1.(b) Find the area of the
Concrete sections for a new building have the dimensions (in meters) and shape shown in the figure.(a) Find the area of the face of the section superimposed on the rectangular coordinate system.(b)
In Exercises evaluate the limit and sketch the graph of the region whose area is represented by the limit. (4- x²) Ax, where x; = − 2 + 4i -2+ and Ax = n lim (4x) ||A||→0 i=1 4 n
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 area of the region bounded by the graphs of ƒ and g is 1,
In Exercises two models R1 and R2 are given for revenue (in billions of dollars) for a large corporation. Both models are estimates of revenues from 2015 through 2020, with t = 15 corresponding to
In Exercises two models R1 and R2 are given for revenue (in billions of dollars) for a large corporation. Both models are estimates of revenues from 2015 through 2020, with t = 15 corresponding to
In Exercises evaluate the limit and sketch the graph of the region whose area is represented by the limit. lim ||A||-0 (x - x²) Ax, where x; = n and Ax = 1 n
A state legislature is debating two proposals for eliminating the annual budget deficits after 10 years. The rate of decrease of the deficits for each proposal is shown in the figure.(a) What does
The chief financial officer of a company reports that profits for the past fiscal year were $15.9 million. The officer predicts that profits for the next 5 years will grow at a continuous annual rate
In Exercises set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point. y 2 1 +
In Exercises set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point. 16x)=22² +1
Two cars with velocities v₁ and v₂ are tested on a straight track (in meters per second). Consider the following. (a) Write a verbal interpretation of each integral.(b) Is it possible to
In Exercises find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area.y² = 4 - x, x = 0 -
In Exercises find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area.y = x, y = 4, x = 0
In Exercises find b such that the line y = b divides the region bounded by the graphs of the two equations into two regions of equal area.y = 9 -|x|, y = 0
Estimate the surface area of the oil spill using (a) The Trapezoidal Rule (b) Simpson’s Rule 4 mi! 11 mi 13.5 mi 14.2 mi 14 mi 14.2 mi 15 mi 13.5 mi
In Exercises find b such that the line y = b divides the region bounded by the graphs of the two equations into two regions of equal area.y = 9 - x², y = 0
The area of the region bounded by the graphs of y = x³ and y = x cannot be found by the single integral ƒ-1, (x3 - x) dx. Explain why this is so. Use symmetry to write a single integral that does
Estimate the surface area of the golf green using (a) The Trapezoidal Rule (b) Simpson’s Rule. 5 ft 14 ft 14 ft 12 ft 12 ft 15 ft 20 ft 23 ft 25 ft 26 ft
The graphs of y = 1 - x² and y = x4 - 2x² + 1 intersect at three points. However, the area between the curves can be found by a single integral. Explain why this is so, and write an integral for
In Exercises find the accumulation function F. Then evaluate F at each value of the independent variable and graphically show the area given by each value of F.(a) F(-1) (b) F(0) (c) F(4)
In Exercises set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point.y = x³ - 2x, (-1, 1)
In Exercises find the accumulation function F. Then evaluate F at each value of the independent variable and graphically show the area given by each value of F.(a) F(0)(b) F(4) (c) F(6) = S²
In Exercises set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point.ƒ(x) = x³, (1, 1)
In Exercises (a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Explain why the area of the region is difficult to find by hand, and (c) Use the
In Exercises find the accumulation function F. Then evaluate F at each value of the independent variable and graphically show the area given by each value of F.(a) F(-1) (b) F(0) (c) F(1/2)
In Exercises use integration to find the area of the figure having the given vertices.(0, 0), (1, 2), (3,-2), (1, -3)
In Exercises use integration to find the area of the figure having the given vertices.(0, 2), (4, 2), (0, -2), (-4,-2)
In Exercises (a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Explain why the area of the region is difficult to find by hand, and (c) Use the
In Exercises find the accumulation function F. Then evaluate F at each value of the independent variable and graphically show the area given by each value of F.(a) F(0)(b) F(2) (c) F(6) F(x) = -
In Exercises use integration to find the area of the figure having the given vertices.(0, 0), (6, 0), (4,3)
In Exercises (a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Explain why the area of the region is difficult to find by hand, and (c) Use the
In Exercises use integration to find the area of the figure having the given vertices.(2,-3), (4, 6), (6, 1)
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Find the area of the region(c) Use the integration capabilities of the graphing utility to verify
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Find the area of the region(c) Use the integration capabilities of the graphing utility to verify
In Exercises sketch the region bounded by the graphs of the functions and find the area of the region. 3 f(x) = 2*, g(x) = x + + 1 2
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Find the area of the region(c) Use the integration capabilities of the graphing utility to verify
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Find the area of the region(c) Use the integration capabilities of the graphing utility to verify
In Exercises sketch the region bounded by the graphs of the functions and find the area of the region. π.Χ. f(x) = sec tan 4 Π.Χ. 4 2 g(x) = (v2 – 4)x + 4, x = 0
In Exercises (a) Use a graphing utility to graph the region bounded by the graphs of the equations(b) Explain why the area of the region is difficult to find by hand, and (c) Use the
In Exercises sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = 2 sin x, g(x) = tan x, T 3
In Exercises sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = xex, y =0, 0 ≤x≤1
In Exercises sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = cos x, g(x) = 2 cos x, 0 ≤ x ≤ 2π
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations (b) Find the area of the region analytically, and (c) Use the integration capabilities of
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations (b) Find the area of the region analytically, and (c) Use the integration capabilities of
In Exercises sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = sin x, g(x) = cos 2x, TT 2 ≤x≤ 6
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations (b) Find the area of the region analytically, and (c) Use the integration capabilities of
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations (b) Find the area of the region analytically, and (c) Use the integration capabilities of
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations (b) Find the area of the region analytically, and (c) Use the integration capabilities of
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. 10 ƒ(x) = ¹0, x = 0, y = 2, y = 10 X
In Exercises(a) Use a graphing utility to graph the region bounded by the graphs of the equations (b) Find the area of the region analytically, and (c) Use the integration capabilities of
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. g(x) 4 2 - x y = 4, x = 0
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. f(y) = y(2-y), g(y) = y
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. f(x) = 3x - 1, g(x) = x - 1
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. f(y) = y 16- y² g(y) = 0, y = 3
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. f(y) = y² + 1, g(y) = 0, y = − 1, y = 2 -
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. y 4 x3, y = 0, x= 1, x = 4
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. f(y) = y², g(y) = y + 2
In Exercises sketch the region bounded by the graphs of the equations and find the area of the region. f(x) = √√√x + 3₂ g(x) = x + 3

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