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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

In Exercises 77–88, factor and simplify the given expression as much as possible. 4(1-x)²(x + 3)³ + 2(1-x)(x + 3)¹ (1-x)4
In Exercises 77–88, factor and simplify the given expression as much as possible.12(x + 3)5(x − 1)3 − 8(x + 3)6(x − 1)2
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. √3-√2 5
In Exercises 83 through 88, use the quadratic formula to solve the given equation.2x2 + 3x + 1 = 0
In Exercises 77–88, factor and simplify the given expression as much as possible. 6(x + 2)²(1 x)4 - 4(x + 2) (1 - x)³ (x + 2)8(1-x)² -
In Exercises 77–88, factor and simplify the given expression as much as possible.x−1/2(2x + 1) + 4x1/2
In Exercises 83 through 88, use the quadratic formula to solve the given equation.−x2 + 3x − 1 = 0
In Exercises 77–88, factor and simplify the given expression as much as possible.x−1/4(3x + 5) + 4x3/4
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. 7 3-√3
In Exercises 83 through 88, use the quadratic formula to solve the given equation.x2 − 2x + 3 = 0
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. √7 +3 2
In Exercises 83 through 88, use the quadratic formula to solve the given equation.x2 − 2x + 1 = 0
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. 5 √5 + √2
In Exercises 83 through 88, use the quadratic formula to solve the given equation.4x2 + 12x + 9 = 0
In Exercises 83 through 88, use the quadratic formula to solve the given equation.x2 + 12 = 0
In Exercises 89 through 94, solve the given system of equations.x + 5y = 133x − 10y = −11
In Exercises 89 through 94, solve the given system of equations.2x − 3y = 4 3x − 5y = 2
In Exercises 89 through 94, solve the given system of equations.5x − 4y = 12 2x − 3y = 2
In Exercises 89 through 94, solve the given system of equations.3x2 − 9y = 0 3y2 − 9x = 0
In Exercises 89 through 94, solve the given system of equations.2y2 − x2 = 1x − 2y = 3
In Exercises 89 through 94, solve the given system of equations.2x2 − y2 = −72x + y = 1
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. 3 T + SA
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. √5 - VII 11 4
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. 5 √5 +1
In Exercises 89 through 96, rationalize the root (or roots) in the given expression. 3 2-√7
Show thatwhere x and h are positive numbers. √x + h-√x = h √x +h+ √x
Simplify the expressionwhere x and h are positive constants. 1 √x + h 1 √x
Show that in the case where m is a negative integer. (x) = x
The atmosphere above each square centimeter of Earth’s surface weighs 1 kilogram (kg).a. Assuming Earth is a sphere of radius R = 6,440 km, use the formula S = 4πR2 to calculate the surface area
In Exercises 1 through 4, use inequalities to describe the indicated interval. -5 X
In Exercises 1 through 4, use inequalities to describe the indicated interval. - 5
In Exercises 1 through 4, evaluate the given sum. 4 Σ (3j + 1) j=1
In Exercises 1 and 2, use inequalities to describe the given interval. f -2 3
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. x²(x - 1) lim x0 3x³ + 2x - 5
In Exercises 1 and 2, use inequalities to describe the given interval.
In Exercises 1 through 4, use inequalities to describe the indicated interval. -5 X
In Exercises 1 through 4, evaluate the given sum. 5 Σ;” j=
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim x→∞0 x² - 2x + 3 2 21² 2x² + 5x + 1
In Exercises 1 through 10, find the indicated product.3x(x − 9)
In Exercises 1 through 10, find the indicated product.−2x2(3 − 4x)
In Exercises 1 through 4, evaluate the given sum. 10 Σ(-1) j=1
In Exercises 1 through 4, use inequalities to describe the indicated interval. X N
In Exercises 1 through 4, evaluate the given sum. 5 Στ j=1
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim x→∞ x² + x - 5 3 1 - 2x - x³
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim 007-X (1/x) - (2/x²) (1/x³) + (2/x²) (3/x)
In Exercises 5 through 10, use summation notation to represent the given sum. 1 + 1 2 + - 3 + - 4 + - 5 + - 6
In Exercises 3 through 6, represent the given interval as a line segment on a number line.−3 ≤ x < 2
In Exercises 1 through 10, find the indicated product.(x − 7)(x + 2)
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. x² + 2x - 15 2 lim 3 x-3 X - 19x + 3
In Exercises 3 through 6, represent the given interval as a line segment on a number line.−1 < x < 5
In Exercises 1 through 10, find the indicated product.(x + 1)(x + 5)
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim X→-1 x³ + 3x² + 3x + 1 2x² + 3x2² - 1
In Exercises 5 through 8, represent the given interval as a line segment on a number line.x ≥ 2
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim x→1/2 -8x² + 2x² + 3x - 1 (2x - 1)³
In Exercises 3 through 6, represent the given interval as a line segment on a number line.x ≥ 1
In Exercises 1 through 10, find the indicated product.(3x − 7)(4 − 2x)
In Exercises 5 through 8, represent the given interval as a line segment on a number line.−6 ≤ x < 4
In Exercises 5 through 10, use summation notation to represent the given sum.3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30
In Exercises 3 through 6, represent the given interval as a line segment on a number line.2 ≤ x < 7
In Exercises 1 through 10, find the indicated product.(−x − 3)(5 − 3x)
In Exercises 5 through 8, represent the given interval as a line segment on a number line.−2 < x ≤ 0
In Exercises 5 through 10, use summation notation to represent the given sum.2x1 + 2x2 + 2x3 + 2x4 + 2x5 + 2x6
In Exercises 7 and 8, find the distance on the number line between the given pair of real numbers.0 and 3
In Exercises 1 through 10, find the indicated product.(x − 1)(x2 + 2x − 3)
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. e -X lim x→∞ 1 +e-2x
In Exercises 5 through 8, represent the given interval as a line segment on a number line.x > 3
In Exercises 5 through 10, use summation notation to represent the given sum.1 − 1 + 1 − 1 + 1 − 1
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim x²e™x 007x
In Exercises 7 and 8, find the distance on the number line between the given pair of real numbers.−5 and −2
In Exercises 1 through 10, find the indicated product.(3x2 − 5x + 4)(x + 2)
In Exercises 9 and 10, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|x − 3| ≤ 1
In Exercises 5 through 10, use summation notation to represent the given sum.1 − 2 + 3 − 4 + 5 − 6 + 7 − 8
In Exercises 9 through 12, find the distance on the number line between the given pair of real numbers.0 and −4
In Exercises 1 through 10, find the indicated product.(x3 − 3x + 4)(x2 − 3x + 2)
In Exercises 9 and 10, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|2x + 1| > 3
In Exercises 5 through 10, use summation notation to represent the given sum.x − x2 + x3 − x4 + x5
In Exercises 9 through 12, find the distance on the number line between the given pair of real numbers.2 and 5
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. Vt lim 1-0 et
In Exercises 11 through 28, simplify the given rational expression. x + 3 x - 3 + X x + 3
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim 00+1 In Vt t
In Exercises 1 through 10, find the indicated product.(2x3 + x2 − 5)(x2 − x − 3)
In Exercises 11 through 20, evaluate the given expression without using a calculator.35
In Exercises 9 through 12, find the distance on the number line between the given pair of real numbers.−2 and 3
In Exercises 11 through 20, evaluate the given expression without using a calculator.4−2
In Exercises 9 through 12, find the distance on the number line between the given pair of real numbers.−3 and −1
In Exercises 11 through 28, simplify the given rational expression. 4 r+5+6 + x - 2 x + 3
In Exercises 11 through 28, simplify the given rational expression. −5r – 6 x²2² + 2x − 3 + x + 2 x - 1
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. lim x¹/x 007-X
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. X z(x up) 04x lim
In Exercises 11 through 20, evaluate the given expression without using a calculator. 4(32)3/4 (V2)³
In Exercises 11 through 28, simplify the given rational expression. x-6 x² + 3x - 10 x +3 X- x - 5
In Exercises 11 through 20, evaluate the given expression without using a calculator. -5/2
In Exercises 11 through 28, simplify the given rational expression. x-2 2x² - 7x - 15 1 2x + 3
In Exercises 1 through 16, use L’Hôpital’s rule to evaluate the given limit if the limit is an indeterminate form. (₁ + 1)²³² X lim 1 +
In Exercises 11 through 20, evaluate the given expression without using a calculator.82/3
In Exercises 13 through 18, find the interval or intervals consisting of all real numbers x that satisfy the given inequality.|x| ≤ 3
In Exercises 11 through 20, evaluate the given expression without using a calculator.49−3/2
In Exercises 11 through 28, simplify the given rational expression. (³² = ³ ) ( ² X 3x x-2
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. 4 x + 2 3 x - 1 2x x² + x -2

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