Problem 3. Recall that a" = for all a > 0 and all b. lim (1+ -)" (1) Compute the limit lim (1+ -)" by carefully performing one step of computation at a time. Try not to skip steps and make sure you understand how each step is justified. (2) Compute the limit lim (1+ -)*+ by writing and using the result you obtained in the previous item. If you follow this instruction, you will find that there is very little to do.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 63RE
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Problem 3. Recall that a = ebIna, for all a > 0 and all b.
(1) Compute the limit
1
lim (1+ -)"
n00
by carefully performing one step of computation at a time. Try
not to skip steps and make sure you understand how each step
is justified.
(2) Compute the limit
lim (1+ )"+1
by writing
(1+ -yn+1
= (1 + )" : (1 +=)
and using the result you obtained in the previous item. If you
follow this instruction, you will find that there is very little to
do.
Transcribed Image Text:Problem 3. Recall that a = ebIna, for all a > 0 and all b. (1) Compute the limit 1 lim (1+ -)" n00 by carefully performing one step of computation at a time. Try not to skip steps and make sure you understand how each step is justified. (2) Compute the limit lim (1+ )"+1 by writing (1+ -yn+1 = (1 + )" : (1 +=) and using the result you obtained in the previous item. If you follow this instruction, you will find that there is very little to do.
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