Consider the following limits. Which of the following is true? Consider the followinglimits:1I : limCOS xx2II: lim x1–¤sin 5xIII : lim2xsin xIV : limx tan x1V : limx→1 In x – sin Tx-sin x2VI : limVII : lim(e" + x)*.x→0 Which of the followingis/are true?1Limit I2A.B. Limit VI = 0.C. Limit IV = 1.D. Limit VI = 2.E. Limit VII = e².Limit IV = 0.F.1G. Limit V1Limit III2.Н.Limit II = e-1.I.1J. Limit V = .1-T'K. Limit VII = 2.Limit III :L.Limit I = 0.M.Limit II = el.N.

Initially, remember the limit formula: limx→a[c·f(x)] =c·limx→a[f(x)] I. limx→01-cosxx2 ⇒1-cos002=00…

Answered: Consider the following limits. Which of…

Math

Advanced Math

Consider the following limits. Which of the following is true?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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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

Consider the following limits. Which of the following is true?

Consider the following
limits:
1
I : lim
COS x
x2
II: lim x1–¤
sin 5x
III : lim
2x
sin x
IV : lim
x tan x
1
V : lim
x→1 In x – sin Tx
-
sin x2
VI : lim
VII : lim(e" + x)*.
x→0

Which of the following
is/are true?
1
Limit I
2
A.
B. Limit VI = 0.
C. Limit IV = 1.
D. Limit VI = 2.
E. Limit VII = e².
Limit IV = 0.
F.
1
G. Limit V
1
Limit III
2.
Н.
Limit II = e-1.
I.
1
J. Limit V = .
1-T'
K. Limit VII = 2.
Limit III :
L.
Limit I = 0.
M.
Limit II = el.
N.

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