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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises, find the indefinite integral. cos t 1+ sin t - dt
In Exercises (a) Verify that ƒ = g by using a graphing utility to graph ƒ and g in the same viewing window (b) Verify that ƒ = g algebraically. ƒ(x) = ln√√x(x² + 1), g(x) = ¹ [ln x + ln(x² + 1)]
In Exercises, find the limit. lim In(6 - x) x-6-
In Exercises, find the indefinite integral. sec x tan x sec x - 1 dx
In Exercises, find the limit. lim In(x - 3) X-3+
In Exercises, find the indefinite integral. csc² t - dt cot t
In Exercises, find the limit. lim In[x²(3 - x)] x-2-
In Exercises, find the indefinite integral. sec x tan x sec x - 1 dx
In Exercises, find the limit. lim In X-5+ X x-4
In Exercises solve the differential equation. Use a graphing utility to graph three solutions, one of which passes through the given point. dy dx || 3 2 - x² (1, 0)
In Exercises, find the indefinite integral. (sec 2x + tan 2x) dx
In Exercises, find the derivative of the function. f(x) = ln(x - 1)
In Exercises, find the derivative of the function. zx u[ = (x)8
In Exercises solve the differential equation. Use a graphing utility to graph three solutions, one of which passes through the given point. dy dx 2x 好 x² - 9x (0,4)
In Exercises solve the differential equation. Use a graphing utility to graph three solutions, one of which passes through the given point. dy dx || x 2 X (-1,0)
In Exercises, find the derivative of the function. y = (In x) 4
In Exercises, find the derivative of the function. y = x² ln x
In Exercises, find the derivative of the function. h(x) = ln(2x² + 1)
In Exercises, find the derivative of the function. y = ln(t + 1)²
In Exercises solve the differential equation. Use a graphing utility to graph three solutions, one of which passes through the given point. dr dt sec² t tant + 1' (T, 4)
In Exercises, find the derivative of the function. y = In(x√x± – 1)
In Exercises, find the derivative of the function. 2 y = In√√x² - 4
In Exercises, find the derivative of the function. f(x) = In 2x x + 3
In Exercises, find the derivative of the function. y In[t(2 + 3)³] =
In Exercises, find the derivative of the function. f(x) = In x² + 1 2
In Exercises, find the derivative of the function. g(t) In t اح
In Exercises, find the derivative of the function. h(t) In t t
In Exercises, find the derivative of the function. y = In, 3, x-1 x + 1
In Exercises, find the derivative of the function. y = ln(In x²)
In Exercises, find the derivative of the function. f(x) = In √4+x² X
In Exercises, find the derivative of the function. y = ln(In x)
In Exercises, find the derivative of the function. y = In. x + 1 x - 1
In Exercises, find the derivative of the function. y = In|sin x
In Exercises, find the derivative of the function. f(x) = ln(x + √√√4 + x²)
In Exercises, find the derivative of the function. y = In|csc x
In Exercises, find the derivative of the function. y = In|csc x
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point y In x³/2, (1,0) =
In Exercises, find the derivative of the function. y = In COS X cos x - 1
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point f(x) = 3x² In x, (1,3)
In Exercises, find the derivative of the function. y = In sec x + tan x|
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point f(x) = 4 - x² - In(x + 1), (0,4)
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point y = ln xt, (1, 0)
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point f(x) = x³ lnx, (1,0)
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point ƒ(x) = x ln x², (-1,0) 1 2 In
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point f(x) = In√1 + sin²x, In 3 2
In Exercises (a) Find an equation of the tangent line to the graph of ƒ at the given point(b) Use a graphing utility to graph the function and its tangent line at the point f(x) = sin 2x In x², (1, 0)
In Exercises use implicit differentiation to find dy/dx. x² - 3 ln y + y² = 10
In Exercises use implicit differentiation to find dy/dx. 4xy + In x²y = 7
In Exercises use implicit differentiation to find dy/dx. x² - 3 ln y + y² = 10
In Exercises, show that the function is a solution of the differential equation. Function y = 2 ln x + 3 Differential Equation xy" + y = 0
In Exercises use implicit differentiation to find dy/dx. In xy + 5x = 30
In Exercises use implicit differentiation to find dy/dx. 4x³+ In y² + 2y = 2x
In Exercises, show that the function is a solution of the differential equation. Function y = x ln x 4x Differential Equation x + y - xy' = 0
In Exercises, show that the function is a solution of the differential equation. Function y = 2 ln x + 3 Differential Equation xy" + y = 0
In Exercises locate any relative extrema and points of inflection. Use a graphing utility to confirm your results. y In x X
In Exercises locate any relative extrema and points of inflection. Use a graphing utility to confirm your results. y cy 2 In x
In Exercises locate any relative extrema and points of inflection. Use a graphing utility to confirm your results. y X In x
In Exercises locate any relative extrema and points of inflection. Use a graphing utility to confirm your results. y 2x In(2x)
In Exercises locate any relative extrema and points of inflection. Use a graphing utility to confirm your results. y = x ln x
In Exercises locate any relative extrema and points of inflection. Use a graphing utility to confirm your results. X y = x² In- 4
In Exercises use a graphing utility to graph the function. Then graphandin the same viewing window. Compare the values of ƒ, P1, P2, and their first derivatives at x = 1. P₁(x) = f(1) + f'(1)(x − 1)
In Exercises use Newton’s Method to approximate, to three decimal places, the x-coordinate of the point of intersection of the graphs of the two equations. Use a graphing utility to verify your result. y = ln x, y = 3 - x
In Exercises use a graphing utility to graph the function. Then graphandin the same viewing window. Compare the values of ƒ, P1, P2,and their first derivatives at x = 1. P₁(x) = f(1) + f'(1)(x − 1)
In Exercises use logarithmic differentiation to find dy/dx. y=x√x² + 1, x > 0
In Exercises use Newton’s Method to approximate, to three decimal places, the x-coordinate of the point of intersection of the graphs of the two equations. Use a graphing utility to verify your result. y = ln x, y = -x
In Exercises use logarithmic differentiation to find dy/dx. y = √√√x²(x + 1)(x + 2), x > 0
In Exercises use logarithmic differentiation to find dy/dx. y x2 / 3x – 2 - (x + 1)2 X > 2/3
In Exercises use logarithmic differentiation to find dy/dx. y = x² - 1 x² + 1' x > 1
In Exercises use logarithmic differentiation to find dy/dx. y = x(x - 1)³/2 √x + 1 x > 1
In Exercises, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. In xy = In x ln y
In Exercises, 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 = In 7, then y' = 1/π.
In your own words, state the properties of the natural logarithmic function.
Define the base for the natural logarithmic function.
In Exercises, 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 = In e, then y' = 1.
The relationship between the number of decibels β and the intensity of a sound I in watts per centimeter squared is(a) Use the properties of logarithms to write the formula in simpler form.(b) Determine the number of decibels of a sound with an intensity of 10-5 watt per square centimeter.
Let ƒ be a function that is positive and differentiable on the entire real number line. Let g(x) = In ƒ(x).(a) When g is increasing, must ƒ be increasing? Explain.(b) When the graph of ƒ is concave upward, must the graphof g be concave upward? Explain.
There are 25 prime numbers less than 100. The Prime Number Theorem states that the number of primes less than approaches(a) x = 1000.(b) x = 1,000,000.(c) x = 1,000,000,000. p(x) X In x
Use a graphing utility to graph ƒ and g in thesame viewing window and determine which is increasing atthe greater rate for large values of x. What can you concludeabout the rate of growth of the natural logarithmic function?(a)(b) f(x) = ln x, g(x) = √ √x
In Exercises, approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. Ső ✓1 + sin² x dx
In Exercises, approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. Cπ/2 √x cos x dx
In Exercises, approximate the definite integral using the Trapezoidal Rule and Simpson's Rule with n = 4. Compare these results with the approximation of the integral using a graphing utility. x3/2 3x² dx
After exercising for a few minutes, a person has a respiratory cycle for which the rate of air intake isFind the volume, in liters, of air inhaled during one cycle by integrating the function over the interval [0, 2]. v = 1.75 sin πt 2
Useto evaluate each definite integral without using the Fundamental Theorem of Calculus.(a)(b)(c)(d) 4 x dx = 32 5
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. X [*cos = dx
In Exercises, find the area of the region. Use a graphing utility to verify your result. #/2 2 Ast 3π 2π -1 [cos x + sin(2x)] dx -2 ➤X
In Exercises, find the area of the region. Use a graphing utility to verify your result. S₁ x x 3√x – 1 dx - 18 15 12 + -6-3 y 9. 6 3 6 9 12
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. π/4 J-T/4 sin 2x dx
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. 2 T J-1 x²√√x + 1 dx
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. 277 S 2π (y + 1)√1-y dy 0
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. C6 13 X 3√√x²-8 dx
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. 1 So vitx 1 + dx
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. [² x²(x³ - 2)³ dx
In Exercises, evaluate the definite integral. Use a graphing utility to verify your result. S б'iзх (3x + 1)5 dx
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the given point. (b) Use integration to find the particular solution of the differential equation
In Exercises, find the indefinite integral. sin x cos x dx
In Exercises a differential equation, a point, and a slope field are given. (a) Sketch two approximate solutions of the differential equation on the slope field, one of which passes through the given point. (b) Use integration to find the particular solution of the differential equation
In Exercises, find the indefinite integral. Гл cos ( 1 sin 0 do
In Exercises, find the indefinite integral. sec 2x tan 2x dx
In Exercises, find the indefinite integral. x sin 3x² dx
In Exercises, find the indefinite integral. fa (1 + sec 7x)² sec πx tan 7x dx
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