FAEN102 - Calculus IExercise 129-Jun-20211) Use the definition of limit to explain what is meant by the limit equationlim f(x) = 4.If the above expression is true, then is it possible that f(1) = 5? Sketch a graphy = f(x) to explain your answer.2) Suppose that the limit of a function f(r) exists at x = a. Iflim f(x) = M andlim f(r) = N,what is the relationship between M and N?3) Suppose that the limit of f(x) exists at z = 1 and letlim f(r) = 5.Find the following limits(a) lim f(z)(b) lim f(r)4) A function f is defined byf(x) Evaluate the following limitsALM & VTTPage 1 of 2(a) lim f(x)(b) lim f(r)(c) lim f(r)5) Given thatf(z) _lim= 3.2 12Find(a) lim f(z)z2+(b) lim f(r)f(z)(c) lim2 (12 – 1)2(d) lim zf(z)6) For the following real valued functions, evaluate each of the indicated limits orexplain why it does not exist.2 – 6z + 9(a) lim1² – 94x2 + 31(b) limz-0 -+ 1z - 2|(c) limz-2 z-212/3 - 4(d) lim(е) lim

In the question we have to find the limit. NOTE - As per Bartleby's policy we can not solve…

1) Use the definition of limit to explain what is meant by the limit equation lim f(z) = 4. If the above expression is true, then is it possible that f(1) = 5? Sketch a graph y = f(z) to explain your answer.

1) Use the definition of limit to explain what is meant by the limit equation lim f(z) = 4. If the above expression is true, then is it possible that f(1) = 5? Sketch a graph y = f(z) to explain your answer.

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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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

FAEN102 - Calculus I
Exercise 1
29-Jun-2021
1) Use the definition of limit to explain what is meant by the limit equation
lim f(x) = 4.
If the above expression is true, then is it possible that f(1) = 5? Sketch a graph
y = f(x) to explain your answer.
2) Suppose that the limit of a function f(r) exists at x = a. If
lim f(x) = M and
lim f(r) = N,
what is the relationship between M and N?
3) Suppose that the limit of f(x) exists at z = 1 and let
lim f(r) = 5.
Find the following limits
(a) lim f(z)
(b) lim f(r)
4) A function f is defined by
f(x)

Evaluate the following limits
ALM & VTT
Page 1 of 2
(a) lim f(x)
(b) lim f(r)
(c) lim f(r)
5) Given that
f(z) _
lim
= 3.
2 12
Find
(a) lim f(z)
z2+
(b) lim f(r)
f(z)
(c) lim
2 (12 – 1)2
(d) lim zf(z)
6) For the following real valued functions, evaluate each of the indicated limits or
explain why it does not exist.
2 – 6z + 9
(a) lim
1² – 9
4x2 + 31
(b) lim
z-0 -+ 1
z - 2|
(c) lim
z-2 z-2
12/3 - 4
(d) lim
(е) lim

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