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Math
Calculus
CALCULUS,EARLY TRANS LCPO
Chapter 1.5, Problem 27E
Chapter 1.5, Problem 27E
BUY
CALCULUS,EARLY TRANS LCPO
9th Edition
ISBN:
9780357771105
Author: Stewart
Publisher:
CENGAGE L
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1 Functions And Models
2 Limits And Derivatives
3 Differentiation Rules
4 Applications Of Differentiation
5 Integrals
6 Applications Of Integration
7 Techniques Of Integration
8 Further Applications Of Integration
9 Differential Equations
10 Parametric Equations And Polar Coordinates
11 Sequences, Series, And Power Series
12 Vectors And The Geometry Of Space
13 Vector Functions
14 Partial Derivatives
15 Multiple Integrals
16 Vector Calculus
A Numbers, Inequalities, And Absolute Values
B Coordinate Geometry And Lines
C Graphs Of Second-degree Equations
D Trigonometry
E Sigma Notation
F Proofs Of Theorems
G The Logarithm Defined As An Integral
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1.1 Four Ways To Represent A Function
1.2 Mathematical Models: A Catalog Of Essential Functions
1.3 New Functions From Old Functions
1.4 Exponential Functions
1.5 Inverse Functions And Logarithms
Chapter Questions
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Problem 1E: (a) What is a one-to-one function? (b) How can you tell from the graph of a function whether it is...
Problem 2E: (a) Suppose f is a one-to-one function with domain A and range B. How is the inverse function f-1...
Problem 3E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 4E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 5E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 6E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 7E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 8E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 9E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 10E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 11E: A function is given by a table of values, a graph, a formula, or a verbal description. Determine...
Problem 12E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 13E: A function is given by a table of values, a graph, a formula, or a verbal description. Determine...
Problem 14E: A function is given by a table of values, a graph, a formula, or a verbal description. Determine...
Problem 15E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 16E: A function is given by a table of values, a graph, a formula or a verbal description. Determine...
Problem 17E: Assume that f is a one-to-one function. (a) If f(6) = 17, what is f1(17)? (b) If f1(3) = 2, what is...
Problem 18E: If f(x) = x5 + x3 + x, find f1(3) and f(f 1(2)).
Problem 19E: If g(x) = 3 + x + ex, find g1(4).
Problem 20E: The graph of f is given. (a) Why is f one-to-one? (b) What are the domain and range of f1? (c) What...
Problem 21E: The formula C=59(F32), where F 459.67, expresses the Celsius temperature C as a function of the...
Problem 22E: In the theory of relativity, the mass of a particle with speed is m=f()=m012/c2 where m0 is the...
Problem 23E: Find a formula for the inverse of the function. 23. f(x)=1x2,x0
Problem 24E: Find a formula for the inverse of the function. 24. g(x)=x22x,x1
Problem 25E: Find a formula for the inverse of the function. 25. g(x)=2+x+1
Problem 26E: Find a formula for the inverse of the function. 26. h(x)=63x5x+7
Problem 27E
Problem 28E
Problem 29E
Problem 30E: Find a formula for the inverse of the function. 26. y=1ex1+ex
Problem 31E: Find an explicit formula for f1 and use it to graph f1, f, and the line y = x on the same screen. To...
Problem 32E: Find an explicit formula for f1 and use it to graph f1, f, and the line y = x on the same screen. To...
Problem 33E
Problem 34E: Use the given graph of f to sketch the graph of f1. 30.
Problem 35E: Let f(x)=1x2,0x1. (a) Find f1. How is it related to f? (b) Identify the graph of f and explain your...
Problem 36E
Problem 37E
Problem 38E: (a) What is the natural logarithm? (b) What is the common logarithm? (c) Sketch the graphs of the...
Problem 39E: Find the exact value of each expression. 39. (a) log381 (b) log3181 (c) log93
Problem 40E
Problem 41E: Find the exact value of each expression. 41. (a) log230log215 (b) log310log35log318 (c)...
Problem 42E
Problem 43E: Use the laws of logarithms to expand each expression. 43. (a) log10x2y3z (b) lnx4x24
Problem 44E
Problem 45E: Express as a single logarithm. 45. (a) log102013log101000 (b) lna2lnb+3lnc
Problem 46E: Express as a single logarithm. 46. (a) 3ln(x2)lnx25x+6+2ln(x3) (b) clogaxdlogay+logaz
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E: Suppose that the graph of y = log2 x is drawn on a coordinate grid where the unit of measurement is...
Problem 52E
Problem 53E
Problem 54E
Problem 55E: (a) What are the domain and range of f? (b) What is the x-intercept of the graph of f? (c) Sketch...
Problem 56E: (a) What are the domain and range of f? (b) What is the x-intercept of the graph of f? (c) Sketch...
Problem 57E
Problem 58E: Solve each equation for x . Give both an exact value and a decimal approximation, correct to three...
Problem 59E: Solve each equation for x . Give both an exact value and a decimal approximation, correct to three...
Problem 60E
Problem 61E: Solve each inequality for x. 55. (a) ln x 0 (b) ex 5
Problem 62E: Solve each inequality for x. 56. (a) 1 e3x1 2 (b) 1 2 ln x 3
Problem 63E: (a) Find the domain of f(x) = ln(ex 3). (b) Find f1 and its domain.
Problem 64E: (a) What are the values of eln 300 and ln(e300)? (b) Use your calculator to evaluate eln 300 and...
Problem 65E: If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of...
Problem 66E: When a camera flash goes off, the batteries immediately begin to recharge the flash's capacitor,...
Problem 67E
Problem 68E: The National Ignition Facility at the Lawrence Livermore National Laboratory maintains the world's...
Problem 69E: Find the exact value of each expression. 63. (a) cos1 (1) (b) sin1(0.5)
Problem 70E: Find the exact value of each expression. 64. (a) tan13 (b) arctan(1)
Problem 71E
Problem 72E: Find the exact value of each expression. 66. (a) sin1(1/2) (b) cos1(3/2)
Problem 73E: Find the exact value of each expression. 67. (a) cot1(3) (b) sec1 2
Problem 74E: Find the exact value of each expression. 68. (a) arcsin(sin(5/4)) (b) cos(2sin1(513))
Problem 75E: Prove that cos(sin1x)=1x2.
Problem 76E: Simplify the expression. 70. tan(sin1 x)
Problem 77E: Simplify the expression. 71. sin(tan1 x)
Problem 78E: Simplify the expression. 72. sin(2 arccos x)
Problem 79E
Problem 80E
Problem 81E: Find the domain and range of the function g(x) = sin1(3x + 1)
Problem 82E: (a) Graph the function f(x) = sin(sin1 x) and explain the appearance of the graph. (b) Graph the...
Problem 83E: (a) If we shift a curve to the left, what happens to its reflection about the line y = x? In view of...
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