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mathematics
calculus 10th edition
Calculus 10th Edition Ron Larson, Bruce H. Edwards - Solutions
In Exercises find the derivative. y = In 1 + ex 1 ex,
In Exercises find the derivative. y = et + 1 et - 1
In Exercises find the derivative. y In (1e2x) =
In Exercises find the derivative. У ex - e-x - 2
In Exercises find the derivative. g(t) = e-3/1²
In Exercises find the derivative. y = x²e-x
In Exercises find the derivative. g(t) = (et + e¹)³
In Exercises find the derivative. y = ex ln x
In Exercises find the derivative. y = ex² +5
In Exercises find the derivative. y = x³ ex
In Exercises find the derivative. y = ex-4
In Exercises find the derivative. y = xe4x
In Exercises find the derivative. y = e-2r³
In Exercises find the derivative. y = e√x
In Exercises find the derivative. y = e-8x
In Exercises illustrate that the functions are inverses of each other by graphing both functions on the same set of coordinate axes. f(x) = ex-1 g(x) = 1 + In x
In Exercises show that ƒ is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = cos x, [0, π]
In Exercises find the derivative. f(x) = ²x 2x
In Exercises illustrate that the functions are inverses of each other by graphing both functions on the same set of coordinate axes. f(x) = ex/3 g(x) = ln x³
In Exercises show that ƒ is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = cotx, (0, TT)
In Exercises illustrate that the functions are inverses of each other by graphing both functions on the same set of coordinate axes. f(x) = ²x g(x) = In√√x
In Exercises illustrate that the functions are inverses of each other by graphing both functions on the same set of coordinate axes. f(x) = ex - 1 g(x) = In(x + 1)
In Exercises match the equation with the correct graph. Assume that a and C are positive real numbers. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d) -2 -1 2 1 -1, y 1 2
In Exercises match the equation with the correct graph. Assume that a and C are positive real numbers. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d) -2 -1 2 1 -1, y 1 2
In Exercises match the equation with the correct graph. Assume that a and C are positive real numbers. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d) -2 -1 2 1 -1, y 1 2
In Exercises match the equation with the correct graph. Assume that a and C are positive real numbers. [The graphs are labeled (a), (b), (c), and (d).](a)(b)(c)(d) -2 -1 2 1 -1, y 1 2
In Exercises sketch the graph of the function. y = e-x²
In Exercises solve for x accurate to three decimal places. 800 100-ex/2 = 50
Use a graphing utility to graph the function. Use the graph to determine any asymptotes of the function.(a)(b) f(x) = 8 1 + e-0.5x
In Exercises sketch the graph of the function. y = ex-1
In Exercises sketch the graph of the function. y = e = x/2
In Exercises sketch the graph of the function. y = ex + 2
In Exercises sketch the graph of the function. y = //ex
In Exercises solve for x accurate to three decimal places. In√x + 2 = 1
In Exercises sketch the graph of the function. y = ex
In Exercises solve for x accurate to three decimal places. In 4x = 1
In Exercises solve for x accurate to three decimal places. In(x - 2)² = 12
In Exercises solve for x accurate to three decimal places. In(x 3) = 2
In Exercises solve for x accurate to three decimal places. In x = 2
In Exercises solve for x accurate to three decimal places. In x² = 10
In Exercises solve for x accurate to three decimal places. 50e-x = 30
In Exercises solve for x accurate to three decimal places. 5000 1 + 2x 2
In Exercises solve for x accurate to three decimal places. 8ex - 12 = 7
In Exercises solve for x accurate to three decimal places. 100e-2x = 35
In Exercises solve for x accurate to three decimal places. 92ex = 7
In Exercises solve for x accurate to three decimal places. 5e* = 36
In Exercises solve for x accurate to three decimal places. ex = 12
In Exercises solve for x accurate to three decimal places. eln 3x = 24
In Exercises solve for x accurate to three decimal places. elnx = 4
Prove that so csc u du = - In|csc u + cot u + C.
Prove that S cot u du = ln sin u + C.
Prove that if a function has an inverse function, then the inverse function is unique.
In Exercises show that ƒ is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = x + 2], [-2,00)
In Exercises show that ƒ is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) حاب x2' (0,00)
In Exercises show that ƒ is strictly monotonic on the giveninterval and therefore has an inverse function on that interval. f(x) = (x-4)², [4,00)
In Exercises show that ƒ and g are inverse functions (a) Analytically (b) Graphically. f(x) = 5x + 1, g(x) = x - 1 5
Show thatis one-to-one and find f(x) = J2 √1 + 1² dt
The demand equation for a product is where p is the price (in dollars) and x is the number (in thousands). Find the average price p on the interval 40 ≤ x ≤ 50. P || 90,000 400 + 3x
Let ƒ be twice-differentiable and one-to-one on an open interval I. Show that its inverse function g satisfiesWhen ƒ is increasing and concave downward, what is the concavity of ƒ-1 = g? g"(x) = f"(g(x)) [f'(g(x))]³*
Find the time required for an object to cool from 300°F to 250°F by evaluatingwhere t is time in minutes. *300 1902 190 250 t= In 1 T - 100 dT
Is the converse of the second part of Theorem 5.7 true? That is, if a function is one-to-one (and therefore has an inverse function), then must the function be strictly monotonic? If so, prove it. If not, give a counterexample.Data from in Theorem 5.7 THEOREM 5.7 The Existence of an Inverse
The rate of change in sales S is inversely proportional to time t (t > 1), measured in weeks. Find S as a function of t when the sales after 2 and 4 weeks are 200 units and 300 units, respectively.
A population of bacteria P is changing at a rate ofwhere t is the time in days. The initial population (when t = 0) is 1000. Write an equation that gives the population at any time t. Then find the population when t = 3 days. dP dt 3000 1 + 0.25t
Prove that a function has an inverse function if and only if it is one-to-one.
In Exercises find the average value of the function over the given interval. f(x) = = sec π.χ. 6 [0, 2]
Prove that if ƒ has an inverse function, then (ƒ-¹)-¹ = ƒ.
In Exercises find the average value of the function over the given interval. f(x) = 4(x + 1) x² [2, 4]
In Exercises find the average value of the function over the given interval. f(x) = 8 x25 [2, 4]
Let ƒ and g be one-to-one functions. Prove that(a) ƒ º g is one-to-one.(b) (ƒ º g)-¹ (x) = (g-¹ º ƒ-¹)(x).
(a) Show that ƒ(x) = 2x³ + 3x² − 36x is not one-to-one on (-∞, ∞).(b) Determine the greatest value c such that ƒ is one-to-oneon (-c, c).
In Exercises show that the two formulas are equivalent. csc x dx = - In|csc x + cotx] + C csc x dx = In|cse x – cot .x| + C
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.There exists no function ƒ such that ƒ = ƒ-¹.
In Exercises show that the two formulas are equivalent. sec x dx = In secx + tan x + C sec x dx = - In secx - tan x] + C
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) = x", where n is odd, then ƒ-¹ exists.
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 the inverse function of ƒ exists, then the y-intercept of ƒ isan x-intercept of ƒ-¹.
In Exercises show that the two formulas are equivalent. [cotx dx cot x dx = In|sin x + C cot x dx = - In|csc x| + C
In Exercises show that the two formulas are equivalent. tan x dx = - In cos x + C tan x dx = In|sec x] + C
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 is an even function, then ƒ-1 exists.
The function ƒ(x) = k(2 - x - x³) is one-to-one and ƒ-¹(3) = -2. Find k.
In Exercises the derivative of the function has the same sign for all x in its domain, but the function is not one-to-one. Explain. f(x) = X x² - 4
Find a value of x such thatis equal to (a) ln 5 (b) 1 x - dt
Find a value of x such that 3 1 [₁²³ a₁ = [₁,₂²7 a ₁. - dt - dt. t 1/4
In Exercises the derivative of the function has the same sign for all x in its domain, but the function is not one-to-one. Explain. f(x) = tan x
Describe the relationship between the graph of a function and the graph of its inverse function.
In Exercises determine which value best approximates the area of the region between the x-axis and the graph of the function over the given interval. (Make your selection on the basis of a sketch of the region, not by performing any calculations.)(a) 3(b) 7(c) -2(d) 5(e) 1 f(x) 2x x² +
In Exercises determine which value best approximates the area of the region between the x-axis and the graph of the function over the given interval. (Make your selection on the basis of a sketch of the region, not by performing any calculations.)(a) 6(b) -6(c) 1/2(d) 1.25(e) 3 f(x) = sec x, [0, 1]
Describe how to find the inverse function of a one-to-one function given by an equation in x and y. Give an example.
In Exercises state the integration formula you would use to perform the integration. Do not integrate. X (x² + 4)³ - dx
In Exercises use the functions ƒ(x) = x + 4 and g(x) = 2x - 5 to find the given function. (gof)-1
In Exercises state the integration formula you would use to perform the integration. Do not integrate. sec² x tan x dx
In Exercises use the functions ƒ(x) = x + 4 and g(x) = 2x - 5 to find the given function. (fog)-1
In Exercises state the integration formula you would use to perform the integration. Do not integrate. √₁² X x² + 4 dx
In Exercises use the functions ƒ(x) = x + 4 and g(x) = 2x - 5 to find the given function. 1 f-log-¹
In Exercises state the integration formula you would use to perform the integration. Do not integrate. [³ 3√/x dx
In Exercises use the functions ƒ(x) = x + 4 and g(x) = 2x - 5 tofind the given function. g-1 of 1
In Exercises use the functions ƒ(x) = 1/8x − 3 and g(x) = x³ to find the given value. (g-¹g-¹)(-4)
In Exercises use the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral. Let n = 4 and round your answer to four decimal places. Use a graphing utility to verify your result. π/3 J-T/3 sec x dx
In Exercises use the functions ƒ(x) = 1/8x − 3 and g(x) = x³ to find the given value. (g-¹g-¹)(-4)
In Exercises (a) Find the domains of ƒ and ƒ-¹(b) Find the ranges of ƒ and ƒ-¹ (c) Graph ƒ and ƒ-¹(d) Show that the slopes of the graphs of ƒ and ƒ-¹ are reciprocals at the given points. Functions f(x)= 4 1 + x²⁹ • f-¹(x) = x ≥ 0 4- x X Point (1, 2) (2, 1)
In Exercises use the functions ƒ(x) = 1/8x − 3 and g(x) = x³ to find the given value. (f-¹ of ¹)(6)
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