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mathematics
calculus with applications

Questions and Answers of Calculus With Applications

If log10 x = −3, what is ln x?
It is estimated that the population of a certain country grows exponentially. If the population was 60 million in 1997 and 90 million in 2002, what will the population be in 2012?
In Exercises 39 through 46, find the largest and smallest values of the given function over the prescribed closed, bounded interval.F(x) = ex2−2x for 0 ≤ x ≤ 2
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
If log5(2x) = 7, what is ln x?
In Exercises 39 through 42, find the effective interest rate re for the given investment.Annual interest rate 6%, compounded quarterly
In Exercises 39 through 42, find the largest and smallest values of the given function over the prescribed closed, bounded interval.f(x) = ln(4x = x2) for 1 ≤ x ≤ 3
If log3(x − 5) = 2, what is ln x?
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 3 through 8, evaluate the given expression using properties of the natural logarithm. e³ Ve In- e¹/3
In Exercises 39 through 42, find the effective interest rate re for the given investment.Annual interest rate 8%, compounded daily (use k = 365)
In Exercises 1 through 38, differentiate the given function.f(x) = ex2 + 2x − 1
In Exercises 1 through 38, differentiate the given function.f(x) = (x2 + 3x + 5)e6x
Find the present value of $8,000 payable 10 years from now if the annual interest rate is 6.25% and interest is compounded:a. Semiannuallyb. Continuously
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.8 = 2e0.04x
In Exercises 1 through 38, differentiate the given function. f(x) = V1 + et
In Exercises 3 through 8, evaluate the given expression using properties of the natural logarithm.e3 ln 2−2 ln 5
In Exercises 5 through 12, evaluate the given expressions. a. 5² b. T T 4/3
In Exercises 5 through 12, evaluate the given expressions.a. (23 − 32)11/7 b. (272/3 + 84/3)−3/2
In Exercises 1 through 38, differentiate the given function.f(x) = xe−x2
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.5 = 1 + 4e−6x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 5 through 12, evaluate the given expressions.a. (33)(3−2) b. (42/3)(22/3)
In Exercises 21 through 36, solve the given equation for x. 1/1/20 = = -1.2x Que
In a classic paper on the theory of conflict,* L. F. Richardson claimed that the proportion p of a population advocating war or other aggressive action at a time t satisfieswhere k and C are positive
In Exercises 1 through 38, differentiate the given function. h(t) e + t In t
In Exercises 1 through 38, differentiate the given function.f(x) = (1 − 3ex)2
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. y = In e3x 1 + x
In Exercises 19 through 28, find all real numbers x that satisfy the given equation. 10 1-2²2² = 1,000
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3 270
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.4 ln x = 8
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.5x = e3
In Exercises 1 through 38, differentiate the given function. f(x) = et + e 2 X
In Exercises 19 through 28, find all real numbers x that satisfy the given equation. 110 8 x-1 23-2²
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. y 3 (x² + €²1)³e-2x 2,2/3 (1 + x -
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3(2.5)
Paul Edwards owns an electronics firm. He determines that when he employs x thousand people, the profit will be P million dollars, whereHow many workers should Paul employ to maximize profit? What is
In Exercises 19 through 28, find all real numbers x that satisfy the given equation. 1-3x² = 34x
When professors select texts for their courses, they usually choose from among the books already on their shelves. For this reason, most publishers send complimentary copies of new texts to
Devi Singh is an efficiency expert working for a major industrial firm. She determines that the daily output of a worker who has been on the job for t weeks is given by a function of the form Q(t) =
In Exercises 1 through 38, differentiate the given function. h(x) = 이외 e X 2
In Exercises 19 through 28, find all real numbers x that satisfy the given equation.10x2−1 = 103
In Exercises 21 through 36, solve the given equation for x. -In x = 50 + C
In Exercises 21 through 36, solve the given equation for x.3 = 2 + 5e−4x
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.yex−x2= x + y
In Exercises 1 through 38, differentiate the given function.g(u) = ln(u2 − 1)3
In Exercises 1 through 38, differentiate the given function. f(t) = √Int + t Vlnt
The economics editor at a major publishing house estimates that if x thousand complimentary copies are distributed to professors, the first-year sales of a certain new text will be f(x) = 15 −
In Exercises 21 through 36, solve the given equation for x.−2 ln x = b
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.xe−y + ye−x = 3
In Exercises 29 through 32, use a graphing calculator to sketch the graph of the given exponential function.y = 31−x
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. У - -Х e x + ln x
When a certain industrial machine has become t years old, its resale value will be V(t) = 4,800e−t/5 + 400 dollars.a. Sketch the graph of V(t). What happens to the value of the machine as t
In Exercises 5 through 12, evaluate the given expressions. a. (3¹-2)(327) 34.1 b. (16)* (125)-26 1/4(125-2/3 81, 8
A toxin is introduced into a bacterial colony, and t hours later, the population is given bya. What was the population when the toxin was introduced?b. When is the population maximized? What is the
In Exercises 19 through 28, find all real numbers x that satisfy the given equation.(2.14)x−1 = (2.14)1−x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 21 through 36, solve the given equation for x.32x−1 = 17
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.y = (1 + e−x)4/5
An archaeological artifact is found to have 45% of its original 14C. How old is the artifact? (Use 5,730 years as the half-life of 14C.)
In Exercises 1 through 38, differentiate the given function.F(x) = ln(2x3 − 5x + 1)
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 19 through 28, find all real numbers x that satisfy the given equation.(3.2)2x−3 = (3.2)2−x
In Exercises 21 through 36, solve the given equation for x.2 = e0.06x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 5 through 12, evaluate the given expressions.a. (32)5/2 b. (e2e3/2)4/3
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5. 64 log:(195)
In Exercises 1 through 38, differentiate the given function.f(x) = e√3x
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.log9(4x − 1) = 2
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions. a. (x + y)⁰ (x²y³) 1/6 b. (x¹¹²)(x² + y²0
In Exercises 9 through 12, use logarithmic rules to rewrite each expression in terms of log3 2 and log3 5.log3 100
In Exercises 1 through 38, differentiate the given function.f(x) = e1/x
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.ln(x − 2) + 3 = ln(x + 1)
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (27x6)2/3 b. (8x2y3)1/3
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 1 through 38, differentiate the given function.f(x) = ln x3
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In x²- X
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.e2x + ex − 2 = 0
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In(x² √4 - x²)
In Exercises 13 through 20, use logarithmic rules to simplify each expression.log2(x4y3)
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (x1/3)3/2 b. (x2/3)−3/4
In Exercises 1 through 38, differentiate the given function. x7²A = (x)ƒ£
In Exercises 1 through 38, differentiate the given function.f(x) = ln 2x
In Exercises 7 through 14, find all real numbers x that satisfy the given equation.e2x + 2ex − 3 = 0
In Exercises 13 through 20, use logarithmic rules to simplify each expression.log3(x5y−2)
In Exercises 1 through 38, differentiate the given function.f(x) = x2 ln x
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.y = x2e−x
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In x²(3 - x)²/3 √x² + x + 1]
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions. a. (x²y3z)³ b. ( 4 -21/6
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (−2t−3)(3t2/3) b. (t−2/3)(t3/4)
In Exercises 13 through 20, use logarithmic rules to simplify each expression. In + Xx X
In Exercises 1 through 38, differentiate the given function. f(x) = In x X
In Exercises 1 through 38, differentiate the given function.f(x) = x ln √x
In Exercises 1 through 38, differentiate the given function. f(x) = In x + 1 x-1,
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation. y = ln Vx² + 4x + 1
In Exercises 15 through 30, find the derivative dy/dx. In some of these problems, you may need to use implicit differentiation or logarithmic differentiation.y = 2e3x + 5
In Exercises 5 through 20, determine where the given function is increasing and decreasing and where its graph is concave upward and concave downward. Sketch the graph of the function. Show as many
In Exercises 13 through 18, use the properties of exponents to simplify the given expressions.a. (t5/6)−6/5 b. (t−3/2)−2/3

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