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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

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.
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)
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)
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
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 ≥
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
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
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
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
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
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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