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study help
mathematics
precalculus
Thomas Calculus Early Transcendentals 13th Edition Joel R Hass, Christopher E Heil, Maurice D Weir - Solutions
Find the indefinite integral. Use a computer algebra system to confirm your result. sec t cost - 1 dt
Find the indefinite integral. Use a computer algebra system to confirm your result. (tan4 t - sec¹ t) dt
Evaluate the definite integral. Use a graphing utility to verify your result. J2/3 (2 - 3t)4 dt
Evaluate the definite integral. Use a graphing utility to verify your result. xp. х xe
Evaluate the definite integral. Use a graphing utility to verify your result. ³ In(x + 1)³ x + 1 - dx
Evaluate the definite integral. Use a graphing utility to verify your result. π/4 cos 2x dx
Evaluate the definite integral. Use a graphing utility to verify your result. π sin² t cost dt
Evaluate the definite integral. Use a graphing utility to verify your result. L₁= ex e²x + 2x + 1 dx
Evaluate the definite integral. Use a graphing utility to verify your result. 2x² + 3x - 2 dx X
Evaluate the definite integral. Use a graphing utility to verify your result. 1 - ln x In X dx
Evaluate the definite integral. Use a graphing utility to verify your result. 8 2x x² + 36 dx
Evaluate the definite integral. Use a graphing utility to verify your result. So 100 10 100x² dx
Evaluate the definite integral. Use a graphing utility to verify your result. (5 2t 1²-4t+4dt
Evaluate the definite integral. Use a graphing utility to verify your result. h = 4x3 x² - 6x² + 9 dx
Evaluate the definite integral. Use a graphing utility to verify your result. (2/√√3 1 10 -dx 4 + 9x²
Use the graph of f shown in the figure to answer the following.(a) Using the interval shown in the graph, approximate the value(s) of x where f is maximum. Explain.(b) Using the interval shown in the graph, approximate the value(s) of x where f is minimum. Explain. и 2 1.0 0.5 f(x) = 8 sin³ x
Using the graph, is positive or negative? Explain. xp (x)f J
Find the area of the given region. y = sin x, y = sin³ x y 1.0 0.5 y = sin x + 14 y = sin³ x IN 2
Find the area of the region bounded by the graphs of the equations. y = cos² x, y = sin² x, x = π 4' X || E|4
Find the area of the given region. y = 0.8 0.6 0.4 0.2 3x + 2 1² + 9 12 3 ч 4 5
Evaluate the definite integral. Use a graphing utility to verify your result. So Jo 7x²+2x(x + 1) dx
Find the area of the region bounded by the graphs of the equations. y = cos² x, y = sin x cos x, X = π 2' X = π +
Find the area of the given region. y = sin² лx 1.0 10.5 y y = sin² x 0.5 1.0 X
Find the area of the given region. y2 = x2(1 - x2) y -2 2 -1 -2 2 X
Find the area of the given region. y = (-4x + 6)3/2 -1 15 10 5 y (1.5, 0) 2 X
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y = tan x, y = 0, x= π 4' X = π :|+
Find the area of the given region. y = sin 2x y 1.0- 0.5 4
Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y-cosy-sin 2' x = 0, x = EIN π 2
Find the centroid of the region bounded by the graphs of y= 1 2x + 1' y = 0, x = 0, and x = 2.
(a) Find ∫cos3 x dx.(b) Find ∫cos5 x dx.(c) Find ∫cos7 x dx.(d) Explain how to find ∫cos15 x dx without actually integrating.
Evaluate the definite integral. Use a graphing utility to verify your result. -0 -4 31-x dx
Sketch the region bounded by the graphs of the equations and find the area of the region. y = 1 x² + 1' y = 0, x= -1, x = 1
Sketch the region bounded by the graphs of the equations and find the area of the region. 금 y = 4, x = 5
Sketch the region bounded by the graphs of the equations and find the area of the region. 7π 3 x = 1/1/12 1/1 ≤ y ≤ ₁ sys 2' 3 x = cos y, x =
Sketch the region bounded by the graphs of the equations and find the area of the region. y sin x, y = cos x, π 4 ≤x≤ 5π 4
Sketch the region bounded by the graphs of the equations and find the area of the region.y = ex, y = e2, x = 0
Determine the work done by the constant force.An electric hoist lifts a 3000-pound car 6 feet.
The area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 5 feet of ethyl alcohol. Find the fluid force on the top side.7. 9 square feet
The area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 5 feet of ethyl alcohol. Find the fluid force on the top side.14 square feet
Sketch the region bounded by the graphs of the equations and find the area of the region. y = csc x, y = 2, π ≤x≤ 5π 6
Find the work done by each force F. (a) F Pounds 4 نيا 2 +++ 1 2 3 4 5 6 Feet x (b) Pounds 4 3 2 1 2 3 4 5 6 Feet X
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 the independent variable. -S 71 (a) F(-л) F(x) (2 + sin t) dt (b) F(0) (c) F(27)
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 the independent variable.(a) F(0) (b) F(2) (c) F(6) - So F(x) = (3t+1) dt
Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2020 through 2025, with t = 0 corresponding to 2020. Which model projects the greater revenue? How much more total revenue does that model project over the six-year
Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2020 through 2025, with t = 0 corresponding to 2020. Which model projects the greater revenue? How much more total revenue does that model project over the six-year
Use the disk method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis. y 1 √√√1 + x² y = 0, x= -1, x x = 1
Use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y 1 x4 + 1' y = 0, x=0, x= 1
Use the disk method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis.y = e-x, y = 0, x = 0, x = 1
Use the shell method to find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the y-axis. y y = 0, x = 2, x = 5
Find the arc length of the graph of the function over the indicated interval. f(x)=x5/4, [0,4]
Find the arc length of the graph of the function over the indicated interval. y = x³/2—1, [2₁6]
Write and evaluate the definite integral that represents the area of the surface generated by revolving the curve on the indicated interval about the y-axis. y = 3√x, 1 ≤ x ≤ 2
The area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 3 feet of water. Find the fluid force on the top side.2 square feet
The area of the top side of a piece of sheet metal is given. The sheet metal is submerged horizontally in 3 feet of water. Find the fluid force on the top side.15 square feet
A circular porthole on a vertical side of a submarine (submerged in seawater) has a diameter of 3 feet. Find the fluid force on the porthole, assuming that the center of the circle is 1600 feet below the surface.
Use the Integral Test to determine if the series converge or diverge. Be sure to check that the conditions of the Integral Test are satisfied. 00 1 Σ n=2 n(In n)²
Use the Ratio Test to determine if each series converges absolutely or diverges. Σ(1)" n=1 n(n + 2)! n! 32n
What is a geometric series? When does such a series converge? Diverge? When it does converge, what is its sum? Give examples.
Gives the first term or two of a sequence along with a recursion formula for the remaining terms. Write out the first ten terms of the sequence.a1 = 1, an+1 = an + (1/2n)
Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at a.ƒ(x) = tan x, a = π/4
What is the nth-Term Test for Divergence? What is the idea behind the test?
Use substitution (as in Example 4) to find the Taylor series at x = 0 of the functions. EXAMPLE 4 Using known series, find the first few terms of the Taylor series for the given function using power series operations. (b) e cos x (a) (2x (2x + x cos x) (a) (2x (2x + x cos x) = (b) e cos x = = 2 = 1
Which of the series converge, and which diverge? Give reasons for your answers. Žen n=1
Use the Limit Comparison Test to determine if each series converges or diverges. ∞ n=1 2n 3 + 4"
Use power series operations to find the Taylor series at x = 0 for the function.x2 sin x
Use the Root Test to determine if each series converges absolutely or diverges. n=1 sin" (₁)
Taylor’s formulaexpresses the value of ƒ at x in terms of the values of ƒ and its derivatives at x = a. In numerical computations, we therefore need a to be a point where we know the values of ƒ and its derivatives. We also need a to be close enough to the values of ƒ we are interested in to
Use any method to determine if the series converges or diverges. Give reasons for your answer. n10 Σ 10" n=1
Find a value for the constant b that will make the radius of convergence of the power seriesequal to 5. ∞ n = 2 = bx In n
List three important considerations that are ignored in the competitive-hunter model.
Find the orthogonal trajectories of the family of curves. Sketch several members of each family.y = cx2
A first-order differential equation of the formis called homogeneous. It can be transformed into an equation whose variables are separable by defining the new variable y = y/x. Then, y = νx andSubstitution into the original differential equation and collecting terms with like variables then gives
Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges. 2 + + 219 + 2 27 + + 2 3n-1 +
Which of the series defined by the formulas converge, and which diverge? Give reasons for your answers. X n=1 an
Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. ∞ 1 Vn Σ(-1)+1. n=1
Use the Integral Test to determine if the series converge or diverge. Be sure to check that the conditions of the Integral Test are satisfied. xo . n=1n²
Use substitution (as in Example 4) to find the Taylor series at x = 0 of the functions. e-5x EXAMPLE 4 Using known series, find the first few terms of the Taylor series for the given function using power series operations. (b) e cos x (a) (2x (2x + x cos x) (a) (2x (2x + x cos x) = (b) e cos x
Use the Ratio Test to determine if each series converges absolutely or diverges. x n=1 n 2₁ n!
Use the Comparison Test to determine if each series converges or diverges. 1 Σ ₂2 n=in? + 30
Gives a formula for the nth term an of a sequence {an}. Find the values of a1, a2, a3, and a4. an = 1 - n n²
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? x n=0
Which of the series defined by the formulas converge, and which diverge? Give reasons for your answers. X n=1 an
Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. 1 Σ(-1)n+1. 13/2 n=1
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an = 1 + (-1)" n
Use the Integral Test to determine if the series converge or diverge. Be sure to check that the conditions of the Integral Test are satisfied. XI 1 70.2 n=1
Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges. 9 + 100 9 + 100² 9 100³ + . + 9 100n + ..
Use substitution (as in Example 4) to find the Taylor series at x = 0 of the functions.e-x/2 EXAMPLE 4 Using known series, find the first few terms of the Taylor series for the given function using power series operations. (b) e cos x (a) (2x (2x + x cos x) (a) (2x (2x + x cos x) = (b) e cos x
Use the Comparison Test to determine if each series converges or diverges. n 1 Σ n=int + 2 2
What is an infinite sequence? What does it mean for such a sequence to converge? To diverge? Give examples.
Gives a formula for the nth term an of a sequence {an}. Find the values of a1, a2, a3, and a4. an 1 n!
(a) Find the series’ radius and interval of convergence. For what values of x does the series converge (b) Absolutely, (c) Conditionally? ∞ Σ(x + 5) X n=0
Which of the sequences whose nth terms appear converge, and which diverge? Find the limit of each convergent sequence. an 1- (-1)" Vn
Use the Ratio Test to determine if each series converges absolutely or diverges. n + 2 3n Σ(1)". n=1 +2
Find a formula for the nth partial sum of each series and use it to find the series’ sum if the series converges. 1 + 2 4 118 + .. + (−1)n-1. + 1 2n-1
Find the Taylor polynomials of orders 0, 1, 2, and 3 generated by ƒ at a.ƒ(x) = e2x, a = 0
Find the first four terms of the binomial series for the function.(1 + x)1/2
Use substitution (as in Example 4) to find the Taylor series at x = 0 of the functions.5sin (-x) EXAMPLE 4 Using known series, find the first few terms of the Taylor series for the given function using power series operations. (b) e cos x (a) (2x (2x + x cos x) (a) (2x (2x + x cos x) = (b) e cos x
Determine if the alternating series converges or diverges. Some of the series do not satisfy the conditions of the Alternating Series Test. 00 n=1 (-1)*+1_1 n3n
Use the Integral Test to determine if the series converge or diverge. Be sure to check that the conditions of the Integral Test are satisfied. 00 n=1 1 n² + 4
What is a monotonic sequence? Under what circumstances does such a sequence have a limit? Give examples.
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