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91,97 please

91,97 please

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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91,97 please
92 Find the value of log2 3 · log3 4· · . •log,(n + 1) · log,+1 2. 100. Find the value of log, 2· log2 4. log2 8. .. • log2 2". Compressing or stretching, and reflecting. State the domain A 128. Is the function f(x) = : SECTION 5.5 Properties of Logarithms 317 88. In y = In (x + C) 90. In y = 2 In x – In (x + 1) + In C 92. In y = -2x + In C 94. In (y + 4) = 5x + In C N7, ln y = In.r + In C 91. In y = 3r + In C et In (y - 3) = -4x + In C + 4) + In C oE 3 In y =, In (2r + 1) - 9%, 2Iny= -imx + 능in (7- + 1) + In C 98. Find the value of log2 4 log4 6 • log, 8. f(x + h) – f(x) h + 0. 106. If f(x) = log, x, show that f(AB) = f(A) + f(B). = -f(x). 1O7. If f(x) = log, X, show that fl 108. If f(x) = log, x, show that f(x") = af(x). = loga M – loga N, where a, M,and N 109. Show that log. are positive real numbers and a 1. 110. Show that log.) = -log, N, where a and N are positive real numbers and a + 1. Ul. Challenge Problem Show that log, b = 112. Challenge Problem Show that log Va m = log, m², where a log, a' and b are positive real numbers, a # 1, and b # 1. where a and m are positive real numbers and a + 1. m 113. Challenge Problem Show that log bm = where a, b, m, and n are positive real numbers, a + 1, and b #1. log, b, 114. Challenge Problem Find n: n log2 3• log3 4. log, 5. ... ·log,(n + 1) = 10 Explaining Concepts: Discussion and Writing 15. Graph Y = log(x²) and Y = 2log (x) using a graphing utility. Are they equivalent? What might 2ccount for any differences in the two functions? 117. Write an example that illustrates why agose log2 (x + y) # log2 x + log2 y 116. Write an example that illustrates why (log, ) rlogax. 118. Does 3log3 (-5) = -5? Why or why not? slda pote noithupa oi Retain Your Knowledge - Olems 119-128 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in Our mind so that you are better prepared for the final exam. ces Use a graphing utility to solve x³ – 3x? – 4xr + 8 = 0. Round answers to two decimal places. N Without solving, determine the character of the solution of he quadratic equation 4x² – 28x + 49 = 0 in the complex number system. 121. Find the real zeros of 123. Find the domain of f(x) = 2V3 – 5x – 4. 124. Solve: 4|x + 1 - 9 < 23 125. Find the vertex of f(x) = --x² + + 4x + 5, and determine if the graph is concave up or concave down. 126. Find the center and radius of the circle x² – 10x + y? + 4y = 35 f(x) = 5x5 + 44x4 + 116x³ + 95x² – 4x – 4 12. Graph f(x) = V2 - x using the techniques of shifting, A 127. Find the average rate of change f(x) = x³ from –1 to 3. even, odd, or neither? 5x? – 3x* and the range of f.
Transcribed Image Text:92 Find the value of log2 3 · log3 4· · . •log,(n + 1) · log,+1 2. 100. Find the value of log, 2· log2 4. log2 8. .. • log2 2". Compressing or stretching, and reflecting. State the domain A 128. Is the function f(x) = : SECTION 5.5 Properties of Logarithms 317 88. In y = In (x + C) 90. In y = 2 In x – In (x + 1) + In C 92. In y = -2x + In C 94. In (y + 4) = 5x + In C N7, ln y = In.r + In C 91. In y = 3r + In C et In (y - 3) = -4x + In C + 4) + In C oE 3 In y =, In (2r + 1) - 9%, 2Iny= -imx + 능in (7- + 1) + In C 98. Find the value of log2 4 log4 6 • log, 8. f(x + h) – f(x) h + 0. 106. If f(x) = log, x, show that f(AB) = f(A) + f(B). = -f(x). 1O7. If f(x) = log, X, show that fl 108. If f(x) = log, x, show that f(x") = af(x). = loga M – loga N, where a, M,and N 109. Show that log. are positive real numbers and a 1. 110. Show that log.) = -log, N, where a and N are positive real numbers and a + 1. Ul. Challenge Problem Show that log, b = 112. Challenge Problem Show that log Va m = log, m², where a log, a' and b are positive real numbers, a # 1, and b # 1. where a and m are positive real numbers and a + 1. m 113. Challenge Problem Show that log bm = where a, b, m, and n are positive real numbers, a + 1, and b #1. log, b, 114. Challenge Problem Find n: n log2 3• log3 4. log, 5. ... ·log,(n + 1) = 10 Explaining Concepts: Discussion and Writing 15. Graph Y = log(x²) and Y = 2log (x) using a graphing utility. Are they equivalent? What might 2ccount for any differences in the two functions? 117. Write an example that illustrates why agose log2 (x + y) # log2 x + log2 y 116. Write an example that illustrates why (log, ) rlogax. 118. Does 3log3 (-5) = -5? Why or why not? slda pote noithupa oi Retain Your Knowledge - Olems 119-128 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in Our mind so that you are better prepared for the final exam. ces Use a graphing utility to solve x³ – 3x? – 4xr + 8 = 0. Round answers to two decimal places. N Without solving, determine the character of the solution of he quadratic equation 4x² – 28x + 49 = 0 in the complex number system. 121. Find the real zeros of 123. Find the domain of f(x) = 2V3 – 5x – 4. 124. Solve: 4|x + 1 - 9 < 23 125. Find the vertex of f(x) = --x² + + 4x + 5, and determine if the graph is concave up or concave down. 126. Find the center and radius of the circle x² – 10x + y? + 4y = 35 f(x) = 5x5 + 44x4 + 116x³ + 95x² – 4x – 4 12. Graph f(x) = V2 - x using the techniques of shifting, A 127. Find the average rate of change f(x) = x³ from –1 to 3. even, odd, or neither? 5x? – 3x* and the range of f.
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