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mathematics
calculus with applications
Calculus With Applications 12th Edition Margaret L. Lial - Solutions
Find the interest rate required for an investment of $5000 to grow to $6100 in 5 years if interest is compounded as follows. (Round percent to nearest hundredth.)(a) Annually (b) Quarterly
Using the graph of f (x) in Figure 10, show the graph of f (ax) where a satisfies the given condition.-1 < a < 0 Figure 10 y=f(x) X
Write an equation that defines a rational function with a vertical asymptote at x = 1 and a horizontal asymptote at y = 2.
Solve each equation in Exercises. Round decimal answers to four decimal places.logx 36 = -2
Assuming continuous compounding, what will it cost to buy a $10 item in 3 years at the following inflation rates?(a) 3% (b) 4% (c) 5%
Solve each equation in Exercises. Round decimal answers to four decimal places.log8 16 = z
Using the graph of f (x) in Figure 10, show the graph of a f (x) where a satisfies the given condition.0 < a < 1 Figure 10 y=f(x) X
Sofia invests a $25,000 inheritance in a fund paying 5.5% per year compounded continuously. What will be the amount on deposit after each time period?(a) 1 year (b) 5 years (c) 10 years
Solve each equation in Exercises. Round decimal answers to four decimal places.log9 27 = m
Write an equation that defines a rational function with a vertical asymptote at x = -2 and a horizontal asymptote at y = 0.
Let f(x) = 6x2 - 2 and g(x) = x2 - 2x + to find the following values. f(x) = 2x + 1 x - 4 7 if x # 4 if x = 4
Andrea plans to invest $600 into a money market account. Find the interest rate that is needed for the money to grow to $1240 in 14 years if the interest is compounded quarterly.
Consider the polynomial functions defined by ƒ(x) = (x - 1)(x - 2)(x + 3), g(x) = x3 + 2x2 - x - 2, and h(x) = 3x3 + 6x2 - 3x - 6.(a) What is the value of ƒ(1)?(b) For what values, other than 1, is ƒ(x) = 0?(c) Verify that g(-1) = g(1) = g(-2) = 0.(d) Based on your answer from part (c),
Use natural logarithms to evaluate each logarithm to the nearest thousandth.log2.80.12
Using the graph of f (x) in Figure 10, show the graph of f (ax) where a satisfies the given condition.0 < a < 1 Figure 10 y=f(x) X
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y -2x + 5 x + 3
Use natural logarithms to evaluate each logarithm to the nearest thousandth.log12 210
Use the ideas in this section to graph each function without a calculator.ƒ(x) = - √2 - x + 2
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y || -х - 4 3x + 6
Use natural logarithms to evaluate each logarithm to the nearest thousandth.log5 30
Use the ideas in this section to graph each function without a calculator.ƒ(x) = - √2 - x - 2
A friend claims that as x becomes large, the expression 1 + 1/x gets closer and closer to 1, and 1 raised to any power is still 1. Therefore, ƒ1x2 = (1 + 1/x)x gets closer and closer to 1 as x gets larger. Use a graphing calculator to graph ƒ on 0.1 ≤ x ≤ 50. How might you use this graph to
Suppose logb 2 = a and logb 3 = c. Use the properties of logarithms to find the following.logb (9b2)
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y = 6 - 3x 4x + 12
Use the ideas in this section to graph each function without a calculator.ƒ(x) = √x + 2 - 3
Explain why 3x > ex > 2x when x > 0, but 3x < ex < 2x when x < 0.
Suppose logb 2 = a and logb 3 = c. Use the properties of logarithms to find the following.logb (72b)
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y 3 - 2x 4x + 20
In Exercises, follow the directions for. y = - √x + 2 - 4 -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
In Exercises, follow the directions fory = √-x + 2 - 4 -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
Use the ideas in this section to graph each function without a calculator.ƒ(x) = √x - 2 + 2
Given the following graph, sketch by hand the graph of the function described, giving the new coordinates for the three points labeled on the original graph. t (-1,4) (-3,-2) 0 X (5,0)
Explain why the exponential equation 4x = 6 cannot be solved using the method described in Example 3.
Suppose logb 2 = a and logb 3 = c. Use the properties of logarithms to find the following.logb 18
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y = x + 1 x = 4
Given the following graph, sketch by hand the graph of the function described, giving the new coordinates for the three points labeled on the original graph. t (-1,4) (-3,-2) 0 X (5,0)
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y = x - 4 x + 1
In our definition of an exponential function, we ruled out negative values of a. The author of a textbook on mathematical economics, however, obtained a “graph” of y = (-2)x by plotting the following points and drawing a smooth curve through them.The graph oscillates very neatly from positive
Suppose logb 2 = a and logb 3 = c. Use the properties of logarithms to find the following.logb 32
Given the following graph, sketch by hand the graph of the function described, giving the new coordinates for the three points labeled on the original graph. t (-1,4) (-3,-2) 0 X (5,0)
Graph each of the following.y = 4e-x/2 - 1
Use the properties of logarithms to write each expression as a sum, difference, or product of simpler logarithms. For example, log2 (√3x) =1/2 log2 3 + log2 x. 9V/5 In #3
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y = 4x 3 - 2x
Use the properties of logarithms to write each expression as a sum, difference, or product of simpler logarithms. For example, log2 (√3x) = 1/2 log2 3 + log2 x. log₁ 15P 72
Graph each of the following.y = -2ex - 3
In Exercises, follow the directions for Exercises 7–12. y = - √x - 2 - 4 -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y 8 5 - 3x
Given the following graph, sketch by hand the graph of the function described, giving the new coordinates for the three points labeled on the original graph.y = -ƒ(x) t (-1,4) (-3,-2) 0 X (5,0)
Use the properties of logarithms to write each expression as a sum, difference, or product of simpler logarithms. For example, log2 (√3x) = 1/2 log2 3 + log2 x. In 3√5 √6
Graph each of the following.y = -3e-2x + 2
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y || 2x x - 3
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y = 2 3 + 2х
Use the properties of logarithms to write each expression as a sum, difference, or product of simpler logarithms. For example, log2 (√3x) = 1/2 log2 3 + log2 x. log3 3р 5k
Graph each of the following.y = 5ex + 2
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. -1 x + 3
In Exercises, follow the directions for. y = √-x - 2 - 4 -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
Solve equation.ex2+5x+6 = 1
Use the properties of logarithms to write each expression as a sum, difference, or product of simpler logarithms. For example, log2 (√3x) =1/2 log2 3 + log2 x.log9(4m)
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y = -4 x + 2
Use the properties of logarithms to write each expression as a sum, difference, or product of simpler logarithms. For example, log2 (√3x) = 1/2 log2 3 + log2 x.log5 (3k)
In Exercises, follow the directions for Exercises 7–12.y = √x - 2 - 4 -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
Write a few sentences describing the relationship between ex and ln x.
Solve equation.8x2 = 2x+4
Solve equation.27x = 9x2+x
Solve equation.5x2+x = 1
Is the “logarithm to the base 3 of 4” written as log4 3 or log3 4?
In Exercises, follow the directions for Exercises 7–12.y = √x + 2 - 4 -10 -10 -10 10 -10 (A) 10 -10 (C) 10 -10 (E) 10 10 10 -10 -10 -10 10 -10 (B) 10 -10 (D) 10 -10 (F) 10 10 10
In Exercises, evaluate each logarithm without using a calculator.ln 1
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept. f(x) = 1/² 2 7/2
Each of the following is the graph of a polynomial function. Give the possible values for the degree of the polynomial, and give the sign ( + or - ) for the leading coefficient. -3-2 -1 50 -50 -100 2 13 4
Solve equation.5-|x| =1/25
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept. f(x) = 1 3 8 x + 3 J 1 3
In Exercises, evaluate each logarithm without using a calculator.ln e5/3
Each of the following is the graph of a polynomial function. Give the possible values for the degree of the polynomial, and give the sign ( + or - ) for the leading coefficient. 1.5 0.5 0 1 2 نا برا X
Solve equation.2|x| = 8
In Exercises, evaluate each logarithm without using a calculator.ln e3
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept. f(x) = 312 -x-4
Each of the following is the graph of a polynomial function. Give the possible values for the degree of the polynomial, and give the sign ( + or - ) for the leading coefficient. 1 -0.5 0 +-0.5 2 3 نرا X
In Exercises, find any horizontal and vertical asymptotes and any holes that may exist for each rational function. Draw the graph of each function, including any x- and y-intercepts. y || 9 - 6x + x² 2 3 - x
In Exercises, evaluate each logarithm without using a calculator.log3 27
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.y = -3x2 - 6x + 4
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept. f(r) = 2 + 6x + 24 +
In Exercises, evaluate each logarithm without using a calculator. logg- 2
In Exercises, match the correct graph A–E to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculataor to check your answers. Each graph in this group is plotted on [-6, 6] by [-6, 6].
In Exercises, evaluate each logarithm without using a calculator.ln e
In Exercises, match the correct graph A–E to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculator to check your answers. Each graph in this group is plotted on [-6, 6] by [-6, 6].
In Exercises, evaluate each logarithm without using a calculator. log₂ 4
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.ƒ(x) = -2x2 + 16x - 21
In Exercises, evaluate each logarithm without using a calculator. log3 1 81
In Exercises, match the correct graph A–E to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculator to check your answers. Each graph in this group is plotted on [-6, 6] by [-6, 6].
In Exercises, evaluate each logarithm without using a calculator. log₂ 1 16
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.ƒ(x) = 2x2 - 4x + 5
In Exercises, match the correct graph A–E to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculator to check your answers. Each graph in this group is plotted on [-6, 6] by [-6, 6].
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.ƒ(x) = -x2 + 6x - 6
In Exercises match the correct graph A–I to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculator to check your answers. Each graph is plotted on [-6, 6] by [-50, 50].y = 0.7x5 - 2.5x4 - x3 + 8x2 + x + 2
In Exercises match the correct graph A–I to the function without using your calculator. Then, after you have answered all of them if you have a graphing calculator, use your calculator to check your answers. Each graph is plotted on [-6, 6] by [-50, 50].y = -x5 + 4x4 + x3 - 16x2 + 12x +
In Exercises, graph each parabola and give its vertex, axis of symmetry, x-intercepts, and y-intercept.ƒ(x) = 2x2 + 8x - 8
Solve equation.ex = 1/e5
Solve equation.3x = 1/81
In Exercises, evaluate each logarithm without using a calculator.log4 64
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