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mathematics
calculus 10th edition

Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions

In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = 4x³ x4
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) 5 - 3x x - 2 X
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = (x² - 4)²
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = x¹/²(x + 3)2/3
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = (x - 3)(x + 2)³
Find the dimensions of the rectangle of maximum area, with sides parallel to the coordinate axes, that can be inscribed in the ellipse given by x2 + 144 16 32 = 1.
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) || 2x 1 + x²
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. 4 f(x) = x³ + x + = X
In Exercises, analyze and sketch a graph of the function. Label any intercepts, relative extrema, points of inflection, and asymptotes. Use a graphing utility to verify your results. f(x) = x² + 1 X
A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see figure). What dimensions should be used so that the enclosed area will be a maximum?
A hallway of width 6 feet meets a hallway of width 9 feet at right angles. Find the length of the longest pipe that can be carried level around this corner. If L is the length of the pipe, show thatwhere θ is the angle between the pipe and the wall of the narrower hallway. (7 - 0) 2 L = 6 csc 0 +
Find the volume of the largest right circular cone that can be inscribed in a sphere of radius r.
In Exercises, approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = x² + x³ 3x² + 2 -
In Exercises, approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = x³ + 2x + 1
In Exercises apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the process until two successive approximations differ by less than 0.001. Let h(x) = ƒ(x) - g(x). f(x) = 1 - x g(x) = x + 2 y -2 f 3 - 1 g 2 X
A right triangle in the first quadrant has the coordinate axes as sides, and the hypotenuse passes through the point (1, 8). Find the vertices of the triangle such that the length of the hypotenuse is minimum.
The wall of a building is to be braced by a beam that must pass over a parallel fence 5 feet high and 4 feet from the building. Find the length of the shortest beam that can be used.
Find the length of the longest pipe that can be carried level around a right-angle corner at the intersection of two corridors of widths 4 feet and 6 feet.
In Exercises, approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = 3√√√x - 1 - x
In Exercises apply Newton's Method to approximate the x-value(s) of the indicated point(s) of intersection of the two graphs. Continue the process until two successive approximations differ by less than 0.001. Let h(x) = ƒ(x) - g(x). f(x) = sin x g(x) = x² - 2x + 1 y 3 نيا 2 00 g 3
Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius r.
In Exercises use the information to evaluate and compare Δy and dy. Function y = 0.5x² x-Value x = 3 Differential of x Ax dx = 0.01
In Exercises use the information to evaluate and compare Δy and dy. Function y = x³ - 6x x-Value x = 2 Differential of .x Ax = dx = 0.1
In Exercises, find the differential dy of the given function. y = 36x²
The radius of a sphere is measured as 9 centimeters, with a possible error of 0.025 centimeter.(a) Use differentials to approximate the possible propagated error in computing the volume of the sphere.(b) Use differentials to approximate the possible propagated error in computing the surface area of
A company finds that the demand for its commodity iswhere p is the price in dollars and x is the number of units. Find and compare the values of Δp and dp as x changes from7 to 8. P = 75 1 4 -X
In Exercises find the tangent line approximation T to the graph of ƒ at the given point. Use this linear approximation to complete the table. X f(x) T(x) 1.9 1.99 2 2.01 2.1
In Exercises find the tangent line approximation T to the graph of ƒ at thegiven point. Use this linear approximation to complete thetable. X f(x) T(x) 1.9 1.99 2 2.01 2.1
In Exercises find the tangent line approximation T to the graph of ƒ at the given point. Use this linear approximation to complete the table. X f(x) T(x) 1.9 1.99 2 2.01 2.1
In Exercises find the tangent line approximation T to the graph of ƒ at the given point. Use this linear approximation to complete the table. X f(x) T(x) 1.9 1.99 2 2.01 2.1
In Exercises find the tangent line approximation T to the graph of ƒ at the given point. Use this linear approximation to complete the table. X f(x) T(x) 1.9 1.99 2 2.01 2.1
In Exercises find the tangent line approximation T to the graph of ƒ at the given point. Use this linear approximation to complete the table. X f(x) T(x) 1.9 1.99 2 2.01 2.1
In Exercises use the information to evaluate and compare Δy and dy. Function y = x³ x-Value x = 1 Differential of x Ax = dx = 0.1
In Exercises find the differential dy of the given function. y = 3x² - 4
In Exercises use the information to evaluate and compare Δy and dy. Function y = 6 - 2x² x-Value x = -2 Differential of .x Ax = dx = 0.1
In Exercises find the differential dy of the given function. y = 3x2/3
In Exercises use the information to evaluate and compare Δy and dy. Function y = x² + 1 x-Value x = -1 Differential of x = dx = 0.01 Ax
In Exercises use the information to evaluate and compare Δy and dy. Function y = 2x4 x-Value x = 2 Differential of x Ax dx = 0.01 =
In Exercises find the differential dy of the given function. y = x tan x
In Exercises find the differential dy of the given function. y = csc 2x
In Exercises find the differential dy of the given function. y=x√1-x²
In Exercises find the differential dy of the given function. y || x+1 2х - 1
In Exercises find the differential dy of the given function. y = √√√√x + 1 X
In Exercises find the differential dy of the given function. y = √9 - x² х
In Exercises find the differential dy of the given function. y = 3x - sin² x
In Exercises find the differential dy of the given function. sec² x x² + 1
In Exercises use differentials and the graph of ƒ to approximate (a) ƒ(1. 9)(b) ƒ(2. 04) 5 4 3 را 2 1 y (2, 1) + 2 3 4 f 5 X
In Exercises use differentials and the graph of ƒ to approximate (a) ƒ(1. 9)(b) ƒ(2. 04) 5 4 3 2 1 y (2, 1) 1 2 3 4 5 -X
In Exercises use differentials and the graph of g' to approximate (a) g(2. 93)(b) g(3. 1)given that g(3) = 8 3 2 1 y g' 2 (3, -1/-) 4 5 X
In Exercises use differentials and the graph of g' to approximate (a) g(2. 93)(b) g(3. 1) given that g(3) = 8 4 3 2 y 2 (3, 3) g + 3 نیا + + 4 5
The graph shows the profit P (in dollars) from selling units of an item. Use the graph to determine which is greater, the change in profit when the production level changes from 400 to 401 units or the change in profit when the production level changes from 900 to 901 units. Explain your reasoning
The measurement of the side of a square floor tile is 10 inches, with a possible error of 1/32 inch.(a) Use differentials to approximate the possible propagated error in computing the area of the square.(b) Approximate the percent error in computing the area of thesquare.
The total stopping distance T of a vehicle iswhere T is in feet and x is the speed in miles per hour. Approximate the change and percent change in total stopping distance as speed changes from x = 25 to x = 26 miles per hour. T = 2.5x + 0.5x2
The measurement of the radius of a circle is 16 inches, with a possible error of 1/4 inch.(a) Use differentials to approximate the possible propagated error in computing the area of the circle.(b) Approximate the percent error in computing the area of thecircle.
The measurements of the base and altitude of a triangle are found to be 36 and 50 centimeters, respectively. The possible error in each measurement is 0.25 centimeter.(a) Use differentials to approximate the possible propagated error in computing the area of the triangle.(b) Approximate the percent
The measurement of the circumference of a circle is found to be 64 centimeters, with a possible error of 0.9 centimeter.(a) Approximate the percent error in computing the area of the circle.(b) Estimate the maximum allowable percent error in measuring the circumference if the error in computing the
In Exercises use differentials to approximate the value of the expression. Compare your answer with that of a calculator. 4/624
The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch.(a) Use differentials to approximate the possible propagated error in computing the volume of the cube.(b) Use differentials to approximate the possible propagated error in computing the surface area
In Exercises use differentials to approximate the value of the expression. Compare your answer with that of a calculator. (2.99)3
In Exercises use differentials to approximate the value of the expression. Compare your answer with that of a calculator. 99.4
In Exercises verify the tangent line approximation of the function at the given point. Then use a graphing utility to graph the function and its approximation in the same viewing window. Function f(x) = √√√x + 4 Approximation X y = 2 + 1 4 Point (0, 2)
The radius of a spherical balloon is measured as 8 inches, with a possible error of 0.02 inch.(a) Use differentials to approximate the possible propagated error in computing the volume of the sphere.(b) Use differentials to approximate the possible propagated error in computing the surface area of
In Exercises use differentials to approximate the value of the expression. Compare your answer with that of a calculator. 3/26
A current of I amperes passes through a resistor of R ohms. Ohm's Law states that the voltage E applied to the resistor isE = IR.The voltage is constant. Show that the magnitude of the relativeerror in R caused by a change in I is equal in magnitude to therelative error in I.
A surveyor standing 50 feet from the base of a large tree measures the angle of elevation to the top of the tree as 71.5°. How accurately must the angle be measured if the percent error in estimating the height of the tree is to be less than 6%?
In Exercises verify the tangent line approximation of the function at the given point. Then use a graphing utility to graph the function and its approximation in the same viewing window. Function f(x) = tan x Approximation y = x Point (0, 0)
In Exercise, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If y is differentiable, then lim (Ay - dy) Ax-0 0.
In Exercises give a short explanation of why the approximation is valid. 4.02~2 + (0.02)
In Exercises give a short explanation of why the approximation is valid. tan 0.05 0 + 1(0.05) ≈
Describe the change in accuracy of dy as an approximation for Δy when Δx isdecreased.
When using differentials, what is meant by the terms propagated error, relative error, and percent error?
In Exercise, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If y = ƒ(x), ƒ is increasing and differentiable, and Δx > 0, then Δy ≥ dy.
Find two positive numbers whose sum is 110 and whose product is a maximum.(a) Analytically complete six rows of a table such as the one below. (b) Use a graphing utility to generate additional rows of the table. Use the table to estimate the solution.(c) Write the product P as a function of
In Exercises complete two iterations of Newton’s Method to approximate a zero of the function using the given initial guess. f(x)=x²5, x₁ = 2.2
In Exercises complete two iterations of Newton’s Method to approximate a zero of the function using the given initial guess. f(x) = x³ 3, x₁ = 1.4 -
In Exercises complete two iterations of Newton’s Method to approximate a zero of the function using the given initial guess. f(x) = cos x, x₁ = 1.6
In Exercises complete two iterations of Newton’s Method to approximate a zero of the function using the given initial guess. 10 = ¹x x = (x)ƒ
In Exercises find two positive numbers that satisfy the given requirements.The sum is S and the product is a maximum.
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = x³ + 4
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = x³ + x - 1
In Exercises find two positive numbers that satisfy the given requirements.The product is 185 and the sum is a minimum.
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = 2x³
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = x² + x - 1
In Exercises find two positive numbers that satisfy the given requirements.The product is 147 and the sum of the first number plus three times the second number is a minimum.
In Exercises find two positive numbers that satisfy the given requirements.The second number is the reciprocal of the first number and the sum is a minimum.
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = 5√√√x - 1 - 2x
In Exercises find two positive numbers that satisfy the given requirements.The sum of the first number and twice the second number is 108 and the product is a maximum.
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x)= x³ 3.9x² +4.79x 1.881
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x)=x2√√x+1
In Exercises find two positive numbers that satisfy the given requirements.The sum of the first number squared and the second number is 54 and the product is a maximum.
In Exercises find the length and width of a rectangle that has the given perimeter and a maximum area.Perimeter: 80 meters
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. x soɔ - x = (x)f
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = x² + x³ - 1
In Exercises find the length and width of a rectangle that has the given perimeter and a maximum area.Perimeter: P units
In Exercises find the point on the graph of the function that is closest to the given point. f(x) = x², (2, 1)
In Exercises approximate the zero(s) of the function. Use Newton’s Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = 1 x + sin x
In Exercises find the length and width of a rectangle that has the given area and a minimum perimeter.Area: 32 square feet
In Exercises find the point on the graph of the function that is closest to the given point. f(x) = (x - 1)², (-5, 3)
In Exercises apply Newton’s Method to approximate the -value(s) of the indicated point(s) of intersection of the two graphs. Continue the process until two successive approximations differ by less than 0.001. Let h(x) = ƒ(x) - g(x).] f(x) = 2x + 1 g(x) = √√√x + 4 3 1 2 g + 3 X
In Exercises find the point on the graph of the function that is closest to the given point. f(x) = √√x, (4,0)

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