2 \n. 1+ - 39. in

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.CT: Chapter Test
Problem 15CT
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For the part circled in orange,  why did we divide by 1/n.? And the part right after that, I'm confused what happened here too.

10.2
0.2.
Let y = n
Then In y :
. By L'Hôpital's rule we have lim
0, so
= lim
lim n2/n = e° = 1.
%3D
10.2.39 Find the limit of the logarithm of the expression, which is n In (1+
-). Using L'Hôpital's rule:
In (1+ 2)
= lim
1
1+(2/n)
-1/n2
lim n ln (1+
= lim
-
1/n
= lim
n→o 1+ (2/n)
= 2.
n 00
Thus the limit of the originol
Transcribed Image Text:10.2 0.2. Let y = n Then In y : . By L'Hôpital's rule we have lim 0, so = lim lim n2/n = e° = 1. %3D 10.2.39 Find the limit of the logarithm of the expression, which is n In (1+ -). Using L'Hôpital's rule: In (1+ 2) = lim 1 1+(2/n) -1/n2 lim n ln (1+ = lim - 1/n = lim n→o 1+ (2/n) = 2. n 00 Thus the limit of the originol
2\n
1+
39.
In
Transcribed Image Text:2\n 1+ 39. In
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