#2:Consider the function f(x) = 2 and the limit lim f(x).X +94x→1(a)Find the maximum value of ð such that | f(x) -< 0.01 if |x – 1| < ð. Give your answer to 4 decimalplaces.(b) True or False? For every M > 0, there exists some N > 0 such that x < -N implies f(x) > M.# 2(a):#2(b): Select v

Answered: #2: Consider the function f(x) = and…

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. Consider the function f(x)= {x+2, x>0 -x-6,x<0. Use the table of values to find the limit of the following: a. lim f(x) x→0+= x 0.0001 0.001 0.01 0.1 1 f(x) b. lim f(x) x→0-= x -1.0 -0.1 -0.01 -0.001 -0.0001 f(x) c. Does the limit f(x) x→0 exist? If yes, give its value. If not, why?
1- give an example of a function with two zeros (f(c)=0), one of which cannot be found by the bisection method (you may sketch a graph.) 2- find the constant c so that the lim_{x->3} (x^2+x+c)/(x^2-5x+6) exists. 3- determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.
Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x) continuous?
Let ƒ(x) = (3x - 1)/x. Make tables of values of ƒ at values of x that approach c = 0 from above and below. Does ƒ appear to have a limit as x→ 0? If so, what is it? If not, why not?
1/(1+e^(1/x)) state the value of each limit. lim f(x) as x -> 0- lim f(x) as x ->0+ lim f(x) as x ->0
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4. Given f(x)= { 1, if x < 0 x-1, if x ≥ 0 , estimate lim f(x) x→0- a.1 b. 0 c. does not exist d. -1 5. Given f(x)= { 1/x, if x < 4 x2, if x ≥ 4 , estimate lim f(x) x→4+ a. 1/4 b. 2 c. does not exist d. 16
Determine value for c so that lim f(x) x--> 3 exists f(x)= 1/3x+c For x<3 -x+8 For x>3
Let h(x) = (x2 - 2x - 3)/(x2 - 4x + 3). a. Make a table of the values of h at x = 2.9, 2.99, 2.999, and so on. Then estimate limx-->3 h(x). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001,......instead? b. Support your conclusions in part (a) by graphing h near c = 3 and using Zoom and Trace to estimate y-values on the graph as x--> 3.
IN THE FOLLOWING PROBLEMS YOU WILL FIND THE LOMIT OF A FUNCTION NUMERICALLY. FIND THE VALUE OF THE LIMIT FROM THE TABLE OF FUNCTIONAL VALUES IN THE TABLE. IF THE LIMIT DOES NOT EXIST. STATE THIS. a) y=cosX-1 : X X -1 -0.5 -0.1 -0.01 0 0.01 0.1 0.5 cos X-1:X 0.04597 0.2448 0.0500 0.0040 UND -0.0050 -0.0500 0.2447 ---- lim cos x-1 : x -------- x--> 0 ---- lim cos x-1 : x x--> 0 ---- lim cos x-1 : x x--> 0
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#2: Consider the function f(x) = and the limit lim f(x). x + %3D x→1 (a) Find the maximum value of d such that f(x) – | < 0.01 if lx – 1l < 8. Give your answer to 4 decimal places. (b) True or False? For every M > 0, there exists some N > 0 such that x < -N implies f(x) > M.