why does the limit not exist without mentioning derivative not existing f (x) – f(a)limx – aAs we know, limits do not always exist. Here are some examples of functions that arenot differentiable at the point x = 1. For each, explain, why the limit above does notexist. Don't explain by saying the derivative doesn't exist - that's circular!1.81.71.61.51.41.31.21.1-1-0.50.511.522.5(a)1.5 Thu Sep 309780501.50.5-0.5-1-2-1(b)23

Answered: Image /qna-images/answer/f8561cfd-8472-4606-ae53-ab6a017835f4.jpg

Answered: does the limit not exist

Math

Calculus

does the limit not exist

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...

See similar textbooks

Similar questions

6. State the definition of the derivative of a function f. Use the definition of the derivative toevaluate limx→0ln(1 + x)xif it exists. If the limit does not exist, explain why.
(a)Find the equation of the tangent line to the curve f(x)=6x^2-5x+3 at the point where x=2. (Use the Basic Differentation Rules to find f'(x). That is, do not use the limit definition (b)Find the equation of the tangent line to thefunction: f(x) = 2x-1/x+2 when x=3
Your job is to find some shortcuts for taking derivatives. For example, if the function is of the form y = c, where c is a constant, then you know the graph is a horizontal line, with a slope of zero, and you don't have to even go through the limit gyrations to get the derivative. Do some experimenting with the limit definition on some easy functions to see what you get. When you post a shortcut, you must also post a good portion of the algebraic (or geometric) argument that supports it. No numerical or graphical (calculator) approximations will count as justification — you need to argue with algebra or geometry.
Sketch the graph of the function defined piecewise by the formulaf(x) = {0, x ≤ −1 ; √1 − x2 , −1 < x < 1 , x, x ≥ 1.b) A positive number _ and the limit L of a function f at a are given. Find a number δ such that|f(x) − L| < _ if 0 < |x − a| < δ. limx→3x2−9x−3= 6; ϵ = 0.05c) Find an equation for the tangent line to the curve y = 2/x at the point (2, 1) on this curve.
F(x) = [x-1 when x<0, 1 when x = 0, x^2 - 1 when x>/= 0 For this function show that f(0) it not equal lim f(x) x-->0
limit of (x + 5) as x approaches to 3 po yung given if ever blurred. ty!
Using the image attatched please find: a. Use the limit definition of the derivative to find f'(x). (please dont use shortcut rules) b. Write the equation of the line tangent to f(x) at the point (1, 4).
Consider the function g(x) = cos(1/x). We will investigate the limit behavior at x = 0. c) If n is an arbitrary positive integer, find points x1 and x2 (int terms of n) in the interval(-1/n, 1/n( such that g(x2) = 1 and g(x2) = -1. d) Explain (in a brief paragraph) why (c) implies that g does not have a limit at x = 0. e) Where is g continuous? Justify your answer. You may use facts from the textbook in Section 2.2 - 2.5.
Use the definition of the derviative to compute the derivative of f(x)= 1-7x2 at the specific point x=2 Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer ). f'(2)=lim→0 (f(2+h)-f(2)) / (h) Part 2: The derivative function Use the definition of the derivative to compute the derivative of the function f(x)1-7x2 at an arbitrary point x=2 Evaluate the limit by using algebra to simplify the difference quotient (in first answer ) and then evaluating the limit (in the second answer). f'(x)= h→0 (f(x+h)-f(x)) / (h) Part 3: The tangent line Now let’s calculate the tangent line to the function f(x)= 1-7x2 at x=5 By using f′(x) from part 2, the slope of the tangent line to f at x=5 is f'(5)= The tangent line to f at x=5 passes through the point (5,f(5)) on the graph of f. (Enter a point in the form (2,3) including the parentheses.) An equation for the tangent line to f…
Limit represents the derivative if sime function f at some number a. State such an f and a in each case
True or Falsea) If the second derivative = 0 at x = a, then you will have an inflection point at x=ab) If the first derivative = 0 at x = a, then you will have a max or a min at x=a c) Polynomial functions will sometimes have vertical asymptotes.d) To determine the behavior of a function near its asymptotes, limits are used. e) For a curve to have a horizontal asymptote, evaluate lim x--> infinity f(x)
Find the limit, if it exists. If the limit does not exist, explain why. limx→∞ x / √x^2+x+1 You must show ALL of your work in order to receive full credit. Do NOT use differentiation. Do NOT use L'Hospital's Rule.