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study help
mathematics
precalculus
Calculus Of A Single Variable 11th Edition Ron Larson, Bruce H. Edwards - Solutions
Use a CAS to evaluate the integrals. p2/TT S x sin dx X
Use reduction formulas to evaluate the integrals. 14 4 tan³ 2x dx
Evaluate the integrals. Some integrals do not require integration by parts. sin 2x cos 4x dx
Use reduction formulas to evaluate the integrals. [8 co 8 cos4 2πt dt
Use reduction formulas to evaluate the integrals. [s sin² 20 cos³ 20 de
Evaluate the integrals. Some integrals do not require integration by parts. [√x √x ln x dx
Find the volume of the solid generated by revolving the region in Exercise 41 about the x-axis.Exercise 41Find the area of the region bounded above by y = 2 cos x and below by y = sec x, -π/4 ≤ x ≤ π/4.
Use reduction formulas to evaluate the integrals. √₂ 2 sin² t sec4 t dt
Evaluate the integrals. Some integrals do not require integration by parts. X xp =
Find the length of the curve y = ln (cos x), 0 ≤ x ≤ π/3.
The average height of American females aged 18–24 is normally distributed with mean μ = 65.5 inches and σ = 2.5 inches.a. What percentage of females are taller than 68 inches?b. What is the probability a female is between 5′1″ and 5′4″ tall?
Find the length of the curve y = ln (sec x), 0 ≤ x ≤ π/4.
At birth, a French citizen has an average life expectancy of 81 years with a standard deviation of 7 years. If 100 newly born French babies are selected at random, how many would you expect to live between 75 and 85 years? Assume life expectancy is normally distributed.
Find the centroid of the region bounded by the x-axis, the curve y = sec x, and the lines x = -π/4, x = π/4.
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. Vx dx 1 + x³
Evaluate the integrals. Some integrals do not require integration by parts. [x²s x² sin x³ dx
The serum cholesterol levels of children aged 12 to 14 years follows a normal distribution with mean μ = 162 mg/dl and standard deviation σ = 28 mg/dl. In a population of 1000 of these children, how many would you expect to have serum cholesterol levels between 165 and 193? between 148 and 167?
The concentration of an antihistamine in the bloodstream of a healthy adult is modeled bywhere C is measured in grams per liter and t is the time in hours since the medication was taken. What is the average level of concentration in the bloodstream over a 6-hr period? C 12.5 4 In (t²- 3t+ 4),
Use reduction formulas to evaluate the integrals. Isi sin 2x dx
Evaluate the integrals. Some integrals do not require integration by parts. I sin sin 3x cos 2x dx
The annual rainfall in inches for San Francisco, California, is approximately a normal random variable with mean 20.11 in. and standard deviation 4.7 in. What is the probability that next year’s rainfall will exceed 17 in.?
Find the area of the region bounded above by y = 2 cos x and below by y = sec x, -π/4 ≤ x ≤ π/4.
The assembly time in minutes for a component at an electronic manufacturing plant is normally distributed with a mean of μ = 55 and standard deviation σ = 4. What is the probability that a component will be made in less than one hour?
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. J-1 V1 + x² sin x dx
Evaluate the integrals. Some integrals do not require integration by parts. (cos √x COS Vx Vx dx
The life expectancy in years of a component in a microcomputer is exponentially distributed, and 1/3 of the components fail in the first 3 years. The company that manufactures the component offers a 1 year warranty. What is the probability that a component will fail during the warranty period?
Express the integrand as a sum of partial fractions and evaluate the integrals. 04 - 40³ + 20² - 30 + 403202 1 (0² + 1)³ dᎾ
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. LE -1 1 + y 1-y dy
Evaluate the integrals. Some integrals do not require integration by parts. 1 x (In x)² dx
Your engineering firm is bidding for the contract to construct the tunnel shown here. The tunnel is 300 ft long and 50 ft wide at the base. The cross-section is shaped like one arch of the curve y = 25 cos (πx/50). Upon completion, the tunnel’s inside surface (excluding the roadway) will be
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. S X4 -2 X² 1 dx
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. √α-DV7²ª² dx (x - 1)√x² - 2x - 48
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. 9x³ - 3x + 1 x³ = x² 43 xp.
Evaluate the integrals. Some integrals do not require integration by parts. finx dx
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. dx (2x + 1)√4x + 4x²
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. 16x³ 4x² - 4x + 1 dx
Evaluate the integrals. Some integrals do not require integration by parts. (In x)³ X dx
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. + y² − 1 y V3 + y dy
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. 203 702 70 + 20 - 5 de
Find, to two decimal places, the areas of the surfaces generated by revolving the curves about the x-axis.y = sin x, 0 ≤ x ≤ π
Evaluate the integrals. Some integrals do not require integration by parts. [x²³e² dx
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. de cos - 1
The mean waiting time to get served after walking into a bakery is 30 seconds. Assume that an exponential density function describes the waiting times.a. What is the probability a customer waits 15 seconds or less?b. What is the probability a customer waits longer than one minute?c. What is the
Use numerical integration to estimate the value ofFor reference, sin-1 0.6 = 0.64350 to five decimal places. sin ¹0.6 0.6 dx 0 V1-x²
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. 214 y³y² + y - 1 S dy
Evaluate the integrals. Some integrals do not require integration by parts. fe x5 et dx
Find, to two decimal places, the areas of the surfaces generated by revolving the curves about the x-axis.y = x2/4, 0 ≤ x ≤ 2
Use numerical integration to estimate the value of π = 4 0 1 1 + x² dx.
According to the U.S. Customs and Border Protection Agency, the average airport wait time at Chicago’s O’Hare International airport is 16 minutes for a traveler arriving during the hours 7–8 a.m., and 32 minutes for arrival during the hours 4–5 p.m. The wait time is defined as the total
Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. J₁ dx 1 + et at
Evaluate the integrals. Some integrals do not require integration by parts. [x³√x² + 1 dx
An average adult under age 60 years assimilates a 12-hr cold medicine into his or her system at a rate modeled bywhere y is measured in milligrams and t is the time in hours since the medication was taken. What amount of medicine is absorbed into a person’s system over a 12-hr period? dy dt 6 In
The lifetime of a $200 printer is exponentially distributed with a mean of 2 years. The manufacturer agrees to pay a full refund to a buyer if the printer fails during the first year following its purchase, and a one-half refund if it fails during the second year. If the manufacturer sells 100
The time between failures of a photocopier is exponentially distributed. Half of the copiers at a university require service during the first 2 years of operations. If the university purchased 150 copiers, how many do you expect to require service during the first year of their operation?
Evaluate the integrals. Some integrals do not require integration by parts. [x² x (In x)² dx
A hydra is a small fresh-water animal, and studies have shown that its probability of dying does not increase with the passage of time. The lack of influence of age on mortality rates for this species indicates that an exponential distribution is an appropriate model for the mortality of hydra. A
Perform long division on the integrand, write the proper fraction as a sum of partial fractions, and then evaluate the integral. 1 2x3 2x² + 1 x - zx dx
The integrals are in no particular order. Evaluate each integral using any algebraic method or trigonometric identity you think is appropriate, and then use a substitution to reduce it to a standard form. Jett ezte² dz
Use the graph of f to find each limit.(a) (b) (c) 6 4 2 2 f(x) = 3 In x 4 4 x-1 |||| 6 8
Evaluate the limit, using L’Hôpital’s Rule if necessary. In x lim x I sin лx Π.Χ.
Find or evaluate the integral by completing the square. 2 -x² + 4x dx
Evaluate the limit, using L’Hôpital’s Rule if necessary. lim x 00 In(et-1)dt X
Evaluate the limit, using L’Hôpital’s Rule if necessary. lim x 1+ Ꮭ cos Ꮎ dᎾ x-1
Solve the equation for x.arcsin√2x = arccos√x
Find the derivative of the function.f (x) = 34x
Find the derivative of the function.y = 5-4x
Find the derivative of the function.y = 63x-4
Find the derivative of the function.f (t) = arccsc(-t2)
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b). lim x 0+ (1 + X, x
Find the derivative of the function.f (x) = x9x
Solve for x accurate to three decimal places.-4 + 3e-2x = 6
Find the derivative of the function.y = -7x(8-2x)
Find the derivative of the function.f (t) = -2t2/8t
Find the derivative of the function.f (t) = 32t/t
Find the derivative of the function.f (x) = arccot √x
Find the derivative of the function.g(t) = t2et
Find the derivative of the function.h(θ) = 2-θ cos πθ
Show that the antiderivatives are equivalent. 3x² √1-16 dx = arcsin x³ + C or arccos √1-x6 + C
Find the derivative of the function.g(x) = ln ex/1 + ex
Find the derivative of the function.g(α) = 5-α/2 sin 2α
Find the derivative of the function.y = √e2x + e-2x
Show that the antiderivatives are equivalent. 6 4 + 9x² dx = arctan + C or arccsc 3x 2 √4 + 9x² 3x + C
Find the derivative of the function.y = log4 (6x + 1)
Find the derivative of the function.h(t) = sin(arccos t)
Find the derivative of the function.h(z) = e-z2/2
The antiderivative ofcan be either arcsin x + C or - arccos x + C. Does this mean that arcsin x = - arccos x? Explain. 1 1-x² dx
Find the derivative of the function.y = log3(x2 - 3x)
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b).lim x 0+ (1 + x)1/x
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b).lim x 0+ 3xx/2
Find the derivative of the function.g(x) = x3/e2x
Use a graphing utility to graph the slope field for the differential equation and graph the particular solution satisfying the specified initial condition. dy dx 10 x 7-1 y(3) = 0
Find the derivative of the function.y = 3e-3/t
Use a graphing utility to graph the slope field for the differential equation and graph the particular solution satisfying the specified initial condition. dy dx 2y √16 16x² y(0) = 2
Find the derivative of the function.g(t) = log2(t2 + 7)3
Use a graphing utility to graph the slope field for the differential equation and graph the particular solution satisfying the specified initial condition. dy dx 1 12 + x² by (4) = 2
Find an equation of the tangent line to the graph of the function at the given point. = arctan (2,
Use a graphing utility to graph the slope field for the differential equation and graph the particular solution satisfying the specified initial condition. dy dx = y(0) 万 1 + x² = 4
Find an equation of the tangent line to the graph of the function at the given point. y 1 4 arccos x, π 2' 6/
Find the derivative of the function.y = log5 √x2 - 1
(a) Describe the type of indeterminate form (if any) that is obtained by direct substitution.(b) Evaluate the limit, using L’Hôpital’s Rule if necessary.(c) Use a graphing utility to graph the function and verify the result in part (b).limx 4+ [3(x - 4)]x-4
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