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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises match the function with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d)ƒ(x) = 3x -4 + -2 6 4 2 y -2+ 2 |x 4
In Exercises sketch the graph of the function by hand.h(x) = 5x-2
In Exercises sketch the graph of the function by hand.y = 3-|x|
In Exercises match the function with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d)ƒ(x) = 3-x -4 + -2 6 4 2 y -2+ 2 |x 4
In Exercises match the function with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d)ƒ(x) = 3x -1 -4 + -2 6 4 2 y -2+ 2 |x 4
In Exercises match the function with its graph. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d)ƒ(x) = 3x-1 -4 + -2 6 4 2 y -2+ 2 |x 4
In Exercises solve for x or b.(a) log10 1000 = x(b) log10 0.1 = x
In Exercises solve for x or b.(a) log3 1/81 = X(b) log6 36 = x
In Exercises solve for x or b.(a) log3 x = -1(b) log2 x = - 4
In Exercises solve for x or b.(a) logb 27 = 3(b) logb 125 = 3
In Exercises solve for x or b.(a) x² - x = log5 25(b) 3x + 5 = log2 64
In Exercises solve for x or b.(a) log3 x + log3(x - 2) = 1(b) log10(x + 3) - log10 x = 1
In Exercises solve the equation accurate to three decimal places.32x = 75
In Exercises solve the equation accurate to three decimal places.56x = 8320
In Exercises solve the equation accurate to three decimal places.23-z = 625
In Exercises solve the equation accurate to three decimal places.3(5x-1) = 86
In Exercises solve the equation accurate to three decimal places. 1 + 0.09 121 12 = 3
In Exercises solve the equation accurate to three decimal places. 1 + 0.10 365 365t = 2
In Exercises solve the equation accurate to three decimal places.log2 (x - 1) = 5
In Exercises solve the equation accurate to three decimal places.log10(t - 3) = 2.6
In Exercises solve the equation accurate to three decimal places. log,√x 4 = 3.2
In Exercises solve the equation accurate to three decimal places.log3 x² = 4.5
In Exercises illustrate that the functions are inverse functions of each other by sketching their graphs on the same set of coordinate axes. f(x) = 4x g(x) = log4x
In Exercises illustrate that the functions are inverse functions of each other by sketching their graphs on the same set of coordinate axes. f(x) = 3x g(x) = log3 x
In Exercises find the derivative of the function.ƒ(x) = 4x
In Exercises find the derivative of the function.ƒ(x) = 34x
In Exercises find the derivative of the function.y = 5-4x
In Exercises find the derivative of the function.y = 63x-4
In Exercises find the derivative of the function.ƒ(x) = x 9x
In Exercises find the derivative of the function.y = x(6-2x)
In Exercises find the derivative of the function. 321 t
In Exercises find the derivative of the function.g(t) = t²2t
In Exercises find the derivative of the function. h(0) 2 cos TO = πθ
In Exercises find the derivative of the function. g(a) = 5-a/2 sin 2a
In Exercises find the derivative of the function. y = log2 (x²-3x)
In Exercises find the derivative of the function. y log4(5x + 1)
In Exercises find the derivative of the function. h(t) = log, (4-1)²
In Exercises find the derivative of the function. -2 y = logs √√x² - 1
In Exercises find the derivative of the function. g(t) = log₂ (t² + 7)³
In Exercises find the derivative of the function. f(x) = log₂ 3/2x + 1
In Exercises find the derivative of the function. f(x) = log₂ x² x - 1
In Exercises find the derivative of the function. h(x) = log3 x√x - 1 2
In Exercises find the derivative of the function. y = log10 x² - 1 X
In Exercises find the derivative of the function. f(t) = 13/2 log₂ √t + 1
In Exercises find the derivative of the function. 4 g(x) = log₁2√√1-x
In Exercises find an equation of the tangent line to the graph of the function at the given point. -x y = 2, (1, 2)
In Exercises find the derivative of the function. g(t) = 10 log t t
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = 5x-2, (2, 1)
In Exercises find an equation of the tangent line to the graph of the function at the given point. y log, x, (27,3) =
In Exercises find an equation of the tangent line to the graph of the function at the given point. y log10 2x, (5, 1) =
In Exercises use logarithmic differentiation to find dy/dx.y = x²/x
In Exercises use logarithmic differentiation to find dy/dx.y = xx-1
In Exercises use logarithmic differentiation to find dy/dx.y = (x - 2)x+1
In Exercises use logarithmic differentiation to find dy/dx.y = (1 + x)¹/x
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = (sin x)x, 크 2²
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = jsin x 2
In Exercises find the indefinite integral. S 3x dx
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = (In x)cos x, (e, 1)
In Exercises find an equation of the tangent line to the graph of the function at the given point. y = x/x, (1, 1)
In Exercises find the indefinite integral. 8-* dx
In Exercises find the indefinite integral. for (x² + 2x) dx
In Exercises find the indefinite integral. (x + 4)6(x+4)² dx
In Exercises find the indefinite integral. fax4 (x4 + 5x) dx
In Exercises find the indefinite integral. x(5-x²) dx
In Exercises find the indefinite integral. 32x 1+ 32x dx
In Exercises evaluate the definite integral. S²₁ -1 2x dx
In Exercises evaluate the definite integral. £* 37/4 -4 3x/4 dx ヤー」
In Exercises find the indefinite integral. 2sin x cos x dx
In Exercises evaluate the definite integral. So (5x - 3x) dx
In Exercises find the area of the region bounded by the graphs of the equations. y = 3, y = 0, x = 0, x = 3
In Exercises evaluate the definite integral. fe (7x - 4x) dx
In Exercises find the area of the region bounded by the graphs of the equations. y = 3cos x sin x, y = 0, x = 0, x = π
Inflation When the annual rate of inflation averages 5% over the next 10 years, the approximate cost C of goods or services during any year in that decade iswhere t is the time in years and P is the present cost.(a) The price of an oil change for your car is presently $24.95. Estimate the price 10
Order the functionsfrom the one with the greatest rate of growth to the one with the least rate of growth for large values of x. f(x) = log₂ x, g(x) = x, h(x) = x², and k(x) = 2x
In Exercises complete the table by determining the balance A for P dollars invested at rate r for t years and compounded n times per year. 11 n A 2 4 12 365 Continuous Compounding
In Exercises complete the table by determining the balance A for P dollars invested at rate r for t years and compounded n times per year. 11 n A 2 4 12 365 Continuous Compounding
In Exercises complete the table by determining the balance A for P dollars invested at rate r for t years and compounded n times per year. 11 n A 2 4 12 365 Continuous Compounding
In Exercises complete the table by determining the amount of money P (present value) that should be invested at rate r to produce a balance of $100,000 in t years.r = 5%Compounded continuously t P 1 10 20 30 40 50
In Exercises complete the table by determining the balance A for P dollars invested at rate r for t years and compounded n times per year. 11 n A 2 4 12 365 Continuous Compounding
In Exercises complete the table by determining the amount of money P (present value) that should be invested at rate r to produce a balance of $100,000 in t years.r = 5%Compounded monthly t P 1 10 20 30 40 50
In Exercises complete the table by determining the amount of money P (present value) that should be invested at rate r to produce a balance of $100,000 in t years.r = 3%Compounded continuously t P 1 10 20 30 40 50
In Exercises complete the table by determining the amount of money P (present value) that should be invested at rate r to produce a balance of $100,000 in t years.r = 2%Compounded daily t P 1 10 20 30 40 50
The graph shows the proportion P of correct responses after n trials in a group project in learning theory.(a) What is the limiting proportion of correct responses as n approaches infinity?(b) What happens to the rate of change of the proportionin the long run? Proportion of correct
Assume that you can earn 6% on an investment, compounded daily. Which of the following options would yield the greatest balance after 8 years?(a) $20,000 now (b) $30,000 after 8 years(c) $8000 now and $20,000 after 4 years(d) $9000 now, $9000 after 4 years, and $9000 after 8 years
Consider a deposit of $100 placed in an account for 20 years at r% compounded continuously. Use a graphing utility to graph the exponential functions describing the growth of the investment over the 20 years for the following interest rates. Compare the ending balances for the three rates.(a) r =
The yield V (in millions of cubic feet per acre) for a stand of timber at age t is V = 6.7e(-48.1)/t, where t is measured in years.(a) Find the limiting volume of wood per acre as t approaches infinity.(b) Find the rates at which the yield is changing when t = 20years and t = 60 years.
The breaking strengths B (in tons) of steel cables of various diameters d (in inches) are shown in the table.(a) Use the regression capabilities of a graphing utility to fit an exponential model to the data.(b) Use a graphing utility to plot the data and graph the model.(c) Find the rates of growth
Complete the table to demonstrate that can also be defined as lim (1 + x)¹/x x→0+
In Exercises find an exponential function that fits the experimental data collected over time t. t y 0 1200.00 1 720.00 2 432.00 3 259.20 4 155.52
In Exercises find an exponential function that fits the experimental data collected over time t. t y 0 600.00 1 630.00 2 661.50 3 694.58 4 729.30
In Exercises find the exact value of the expression.51/In 5
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. 271,801 99,900
In Exercises find the exact value of the expression.6In 10/In 6
In Exercises find the exact value of the expression.91/In 3
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.The exponential function y = Cex is a solution of the differential equation dny dxn y, n = 1, 2, 3, .
In Exercises find the exact value of the expression.321/In 2
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 ƒ(x) = In x, then ƒ(en+1) - ƒ(en) = 1 for any value of n.
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.The functions ƒ(x) = 2 + ex and g(x)= In(x - 2) are inverse functions of each other.
Letfor a > 0, a ≠ 1. Show that ƒ has an inverse function. Thenfind ƒ-¹. f(x) = a – 1 a + 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.The graphs of ƒ(x) = ex and g(x) = e-x meet at right angles.
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