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7n3 + 2n An Зп3 — 4 3n3 - 4

7n3 + 2n An Зп3 — 4 3n3 - 4

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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Question 1: Give the limit of the following sequences. nV14 – 3n2 + T C, = 7n3 + 2n 2nT An = 3n3 – 4 В, — sin 3 n" + 2nv2 +1 Vn2 + 5 – n, 3n + 2(-1)" Dn = En = V n? + 3n – n, Fn = n7 Question 2: Which of the following sequences are increasing, decreasing, or bounded? 1 Gn = 5 – (-1)" Hn = In = n3 n Jn = sin Kn = (-5)", Ln = 3-n Question 3: Let k > 0. Vk2 + 3x2 – k (a) Give A = lim x2 (b) Sketch the graph of the function f(x) = (x – 1)-1(x – 2)-2, indicating the asymptotes and critical points. Question 4: (a) Let f and g be functions such that f(x)< g(x) for all x in the interval (a, b), (with a < b). Show that if L = lim f(x) and M = lim g(x) xa+ both exist, then L< M. (b) Using the formal definition of limit, show that if lim an = +0 and r < 0, then lim r an = -00.
Transcribed Image Text:Question 1: Give the limit of the following sequences. nV14 – 3n2 + T C, = 7n3 + 2n 2nT An = 3n3 – 4 В, — sin 3 n" + 2nv2 +1 Vn2 + 5 – n, 3n + 2(-1)" Dn = En = V n? + 3n – n, Fn = n7 Question 2: Which of the following sequences are increasing, decreasing, or bounded? 1 Gn = 5 – (-1)" Hn = In = n3 n Jn = sin Kn = (-5)", Ln = 3-n Question 3: Let k > 0. Vk2 + 3x2 – k (a) Give A = lim x2 (b) Sketch the graph of the function f(x) = (x – 1)-1(x – 2)-2, indicating the asymptotes and critical points. Question 4: (a) Let f and g be functions such that f(x)< g(x) for all x in the interval (a, b), (with a < b). Show that if L = lim f(x) and M = lim g(x) xa+ both exist, then L< M. (b) Using the formal definition of limit, show that if lim an = +0 and r < 0, then lim r an = -00.
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