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6. Compute n2 + ! lim n+00 n3 + sin n

6. Compute n2 + ! lim n+00 n3 + sin n

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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1. Find the sum of all integers points in the domain of the function 2 arcsin ( If there is an infinite number of integer points, write T. 2. Which one is the correct statement for the sequence that does not have a limit? VC Vn e N3E > 0 = |a, – C| > e 3e > 0 VN € N En > N = |a,n C| > ɛ O Je > 0 3n >N = |a, – C| > E Nothing of the above 3. Fill in the blanks: "Let us prove that 2 + V3 is not ***** Assume the opposite: V2 + V3 = ", where $m$ is ***** and n is ***** Squaring both sides, we get 5 + 2/6 = m, or V6 = D (-5). Since (플-5) is ***** we get equivalent to the v2 case." Write missing words in the order of blanks, separate with semicolon, for each blank there should be only one word. Please use these word options: natural, integer, rational or real. Please note that words can be repeated. 4. Assume that you have a graph of f(x) function and you need to plot g(x) = 2 – f(4+ 3x) using simple graph transitions. What is the right order of transitions: shrink horizontally by 3; move horizontally by 4; turn the graph upside-down (multiply by (-1)); move vertically up by 2 O move horizontally by 4/3; shrink horizontally by 3; move vertically down by 2; turn the graph upside-down (multiply by (-1) both variants are wrong 5. Consider a, = 2n. Let us prove by the definition that the limit equals to 0. For e = 10-3 find the smallest N(e) that Ja, < e for alln > N. 6. Compute n? lim n-00 n3 + sin n 1 7. Compute lim (1 - )" Please note that if you want to use mathematical constant e you need to write big 'E'.
Transcribed Image Text:1. Find the sum of all integers points in the domain of the function 2 arcsin ( If there is an infinite number of integer points, write T. 2. Which one is the correct statement for the sequence that does not have a limit? VC Vn e N3E > 0 = |a, – C| > e 3e > 0 VN € N En > N = |a,n C| > ɛ O Je > 0 3n >N = |a, – C| > E Nothing of the above 3. Fill in the blanks: "Let us prove that 2 + V3 is not ***** Assume the opposite: V2 + V3 = ", where $m$ is ***** and n is ***** Squaring both sides, we get 5 + 2/6 = m, or V6 = D (-5). Since (플-5) is ***** we get equivalent to the v2 case." Write missing words in the order of blanks, separate with semicolon, for each blank there should be only one word. Please use these word options: natural, integer, rational or real. Please note that words can be repeated. 4. Assume that you have a graph of f(x) function and you need to plot g(x) = 2 – f(4+ 3x) using simple graph transitions. What is the right order of transitions: shrink horizontally by 3; move horizontally by 4; turn the graph upside-down (multiply by (-1)); move vertically up by 2 O move horizontally by 4/3; shrink horizontally by 3; move vertically down by 2; turn the graph upside-down (multiply by (-1) both variants are wrong 5. Consider a, = 2n. Let us prove by the definition that the limit equals to 0. For e = 10-3 find the smallest N(e) that Ja, < e for alln > N. 6. Compute n? lim n-00 n3 + sin n 1 7. Compute lim (1 - )" Please note that if you want to use mathematical constant e you need to write big 'E'.
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