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mathematics
calculus with applications
Calculus For Business, Economics And The Social And Life Sciences 11th Brief Edition Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price - Solutions
In Exercises 11 through 20, evaluate the given expression without using a calculator. 23/2 (45/2) 82/3
In Exercises 13 through 18, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|x + 4| ≤ 2
In Exercises 11 through 28, simplify the given rational expression. 4 x + 3 2 x + 4 2x + 3 x² + 7x + 12
In Exercises 11 through 28, simplify the given rational expression. -2 x - 4 + 1 x + 4 + 1 - 2x 2 x² - 16
In Exercises 11 through 20, evaluate the given expression without using a calculator. √54 V/2 V8
In Exercises 13 through 18, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|1 − x| < 3
In Exercises 11 through 28, simplify the given rational expression. 7 x - 1 + 5 2x + 3 x + 2 2x² + x3
In Exercises 11 through 20, evaluate the given expression without using a calculator. √81(6²/3) 24/3
In Exercises 11 through 20, evaluate the given expression without using a calculator.163/2 + 272/3
In Exercises 13 through 18, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|x + 2| ≥ 5
In Exercises 11 through 28, simplify the given rational expression. 1/x 1/3 1/x + 1/3
In Exercises 13 through 18, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|x - 1|> 3
In Exercises 21 through 24, solve the given equation for n (assume a > 0, a ≠ 1) a³ (Va)³ 5 = 2n
In Exercises 11 through 28, simplify the given rational expression. 1/x 1 + (1/x)
In Exercises 19 through 26, evaluate the given expression without using a calculator.53
In Exercises 19 through 26, evaluate the given expression without using a calculator.2−3
In Exercises 21 through 24, solve the given equation for n (assume a > 0, a ≠ 1)a2/3a1/2 = a3n
In Exercises 11 through 28, simplify the given rational expression. x - 3 x + 3 X x - 3 x + 3 x - 3 X x + 3
In Exercises 19 through 26, evaluate the given expression without using a calculator.161/2
In Exercises 19 through 26, evaluate the given expression without using a calculator.36−1/2
In Exercises 21 through 24, solve the given equation for n (assume a > 0, a ≠ 1)a2a−5 = (an)3
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 + 8x + 12
In Exercises 29 and 30, express the given sum in terms of the summation notation. 1 + 1 2 - 3 + 4 5 + 6 7
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 + x − 2
In Exercises 29 and 30, express the given sum in terms of the summation notation.3 + 12 + 27 + 48 + 75
In Exercises 11 through 28, simplify the given rational expression. 3x² + 5x - 8 ²³-1 3x + 8 x² + x + 1
In Exercises 25 through 28, evaluate the given sum. 3 (2k + 3) k=1
In Exercises 19 through 26, evaluate the given expression without using a calculator. 4 1/2
In Exercises 25 through 28, evaluate the given sum. 4 Σ ( + 1)2 k k=1
In Exercises 11 through 28, simplify the given rational expression. 3+ 1 5 x - 1 x + 1
In Exercises 11 through 28, simplify the given rational expression. 1 1 + 1 X 2x - 1
In Exercises 11 through 28, simplify the given rational expression. 1 X 2+ X x + 1 3x - 1 x² + x 2
In Exercises 19 through 26, evaluate the given expression without using a calculator. -3/2
In Exercises 25 through 28, evaluate the given sum. 5 Σ (2k2 – k) k=1
In Exercises 19 through 26, evaluate the given expression without using a calculator.82/3
In Exercises 21 through 24, solve the given equation for n (assume a > 0, a ≠ 1)a2na3 = a−7
In Exercises 27 through 34, evaluate the given expression without using a calculator. 25 (2²) 28
In Exercises 25 through 28, evaluate the given sum. 4 k 1 k= 1 k+3 12
In Exercises 11 through 28, simplify the given rational expression. X 1² 2 - 9 1 x + 3 3 x - 3
In Exercises 19 through 26, evaluate the given expression without using a calculator.27−4/3
In Exercises 27 through 34, evaluate the given expression without using a calculator. 34 (3³) (3²)³
In Exercises 27 through 34, evaluate the given expression without using a calculator. 24/3(25/3) 25
In Exercises 27 through 34, evaluate the given expression without using a calculator. 5-³(5²) (5-2)³
In Exercises 27 through 34, evaluate the given expression without using a calculator. 2(163/4) 23
In Exercises 27 through 34, evaluate the given expression without using a calculator. √27 (√3)³ 9
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 + 3x − 10
In Exercises 31 through 34, factor the given expression.x4 − 9x2
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 − 7x + 12
In Exercises 35 and 36, simplify the given quotient as much as possible. x²(x - 1)³2x(x − 1)² - x²2² - x - 2
In Exercises 31 through 34, factor the given expression.x3 + 3(x − 12)
In Exercises 35 and 36, simplify the given quotient as much as possible. x(x + 2)² = x²(x + 2)² x² + 3x + 2
In Exercises 31 through 34, factor the given expression.x16 − (2x)4
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 − 2x + 1
In Exercises 27 through 34, evaluate the given expression without using a calculator.[√8 (25/2)]−1/2
In Exercises 31 through 34, factor the given expression.2(x − 3)2(x + 1) − 5(x − 3)3(2x)
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x2 + 6x + 9
In Exercises 27 through 34, evaluate the given expression without using a calculator.[√27 (35/2)]1/2
In Exercises 29 through 58, factor the given polynomial using integer coefficients.16x2 − 25
In Exercises 35 through 42, solve the given equation for n. (Assume a > 0 and a ≠ 1.)a3a7 = an
In Exercises 29 through 58, factor the given polynomial using integer coefficients.3x2 − x − 14
In Exercises 35 through 42, solve the given equation for n. (Assume a > 0 and a ≠ 1.)a5/a2 = an
In Exercises 37 through 42, factor the given polynomial using integral coefficients.x2 + 2x − 15
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x3 − 1
In Exercises 35 through 42, solve the given equation for n. (Assume a > 0 and a ≠ 1.)a4a−3 = an
In Exercises 37 through 42, factor the given polynomial using integral coefficients.2x2 + 5x − 3
In Exercises 29 through 58, factor the given polynomial using integer coefficients.x3 − 27
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. x-² - 9 dx
Show that a uniformly distributed random variable X with probability density functionhas expected value 1 f(x) = b - a 0 if a ≤ x ≤ b otherwise
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. √4x² - 9 - dx
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. dx (9 + 2x²)3/2
Use the trapezoidal rule with n = 8 to estimate the area bounded by the curve ,the x axis, and the lines x = 0 and x = 1. y = √x²³ + 1,
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. t dt V4 - 5t
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. *00 xex dx
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. du 16 - 3 2 Зи
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. L. 1 -∞0 (2x - 1)² dx
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. •+∞0 In x Vx dx
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. we -3w dw
The useful life of a particular type of printer is measured by a random variable X with probability density functionwhere x denotes the number of months a randomly selected printer has been in use.a. What is the probability that a randomly selected printer will last between 10 and 15 months?b. What
In Exercises 27 through 32, find the expected value for the random variable with the density function given in the indicated problem.a. P(0 ≤ X ≤ 4)b. P(2 ≤ X ≤ 3)c. P(X ≥ 1) f(x): = (4x) if 0≤x≤ 4 8 0 otherwise
In Exercises 27 through 32, find the expected value for the random variable with the density function given in the indicated problem.a. P(0 ≤ X ≤ 4)b. P(1 ≤ X ≤ 2)c. P(X ≤ 1) 3 (4x - x²) if 0≤x≤ 4 otherwise f(x)=32 0
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. fx²√2 + 5x dx
Use the trapezoidal rule with n = 10 to estimate the average value of the functionthe interval 1 ≤ x ≤ 6. f(x): e -0.4.x X over
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. (In x)³ dx
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. ∞o +. I-Xot. 10 x + 2 dx
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. 00 L -00 x²³ex dx
In Exercises 27 through 32, find the expected value for the random variable with the density function given in the indicated problem.a. P(1 ≤ X b. P(1 ≤ X ≤ 2)c. P(X ≥ 2) 3 f(x) = {x² 0 if x ≥ 1 if x < 1
In Exercises 1 through 30, either evaluate the given improper integral or show that it diverges. L X -∞0 (x² + 1)³/2' dx
Use the trapezoidal rule with n = 6 to estimate the average value of the function over the interval 1 ≤ x ≤ 4. y = Vln x
Use the trapezoidal rule with n = 7 to estimate the volume of the solid generated by rotating the region under the curve between x = 0 and x = 1 about the x axis. y = x 1 + x
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. -1 -0 xex+1 dx
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. L -00 ,2x 1 (x - 1)² dx
In Exercises 27 through 32, find the expected value for the random variable with the density function given in the indicated problem.a. P(0 ≤ X b. P(X ≤ 2)c. P(X ≥ 5) f(x) = 10 0 -x/10 if x ≥ 0 if x < 0
The life span of the lightbulbs manufactured by a certain company is measured by a random variable X with probability density functionwhere x denotes the life span (in hours) of a randomly selected bulb.a. What is the probability that the life span of a randomly selected bulb is between 50 and 60
The useful life X of a particular kind of machine is a random variable with density functionwhere x is the number of years a randomly selected machine stays in use.a. Find the probability that a randomly selected machine will be useful for more than 4 years.b. Find the probability that a randomly
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. dx x²(5 + 2x)²
Harriet Truscott, a wealthy patron of a small private college, wishes to endow a chair in mathematics. Suppose the mathematician who occupies the chair is to receive $70,000 per year in salary and benefits. If the gift can be invested at an annual interest rate of 8% compounded continuously, how
In Exercises 21 through 34, either evaluate the given improper integral or show that it diverges. [(e² + (et + ex) dx
An investment will generate $2,400 per year in perpetuity. If the money is dispensed continuously throughout the year and if the prevailing annual interest rate remains fixed at 4% compounded continuously, what is the present value of the investment?
In Exercises 35 through 38, integrate the given probability density functions to find the indicated probabilities.a. P(1 ≤ X ≤ 4) b. P(2 ≤ X ≤ 3)c. P(X ≤ 2) f(x) = if 1 ≤ x ≤ 4 3 0 otherwise
Use the table of integrals (Table 6.1) to find the integrals in Exercises 27 through 38. V9- √9-1² X dx
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