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Textbook not clear please help explain this question(s)

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[SOLVED] Textbook not clear.... please help explain this question(s)...

Question 1.

1. Homework Statement

State whether the limit exists for (Limit as x aproaches infinity ==> (n+1)/(n+1)

and give the value of it if it does exist. Graph the first 5 terms of each sequence.


3. The Attempt at a Solution


if you use any number for "n", numerator divided by denominator would equal 1.


Question 2:



1. Homework Statement
The sequence a1, a2, a3 ..... has the following possible nth terms. For the case given below try various large values for n and guess the limit. Confirm that guess by manipulating the general term an.

a(n) = (n+1) / (n^2+1)





I'm taking a intro Calc class, so this is probably easy stuff for you guys, that's why I lumped both questions into one thread. Anhow, I'm not looking for an answer since it's in my book, I just want to know what the question is asking for.
 

Answers and Replies

131
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and.... where's that thread that explains how to use syntax.


edit: nm, I just found it....latex not syntax lol
 
Dick
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So what's your question? Did you follow the suggestion and substitute various values of n? What's your guess of the limit?
 
131
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question 1: limit equals 1?
 
131
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question 2:


answer:

an = n + 1 / n^2 + 1

possible answers: 11/101, 101/10001, 1001/1000001 appears to have limit of zero?


but how does it have limit of zero?
 
Dick
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Yep. Can you prove it? Divide numerator and denominator by n.
 
Dick
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question 2:


answer:

an = n + 1 / n^2 + 1

possible answers: 11/101, 101/10001, 1001/1000001 appears to have limit of zero?


but how does it have limit of zero?
Same answer, yes. Can you prove it? Divide numerator and denominator by n^2.
 
131
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oh wait....question 2's answer is from the book, not mine.

I attempted it the same way..............except


what I don't understand is how it has a limit of zero?
 
Dick
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Ok, divide numerator and denominator of 2) by n^2. This gives you (1/n+1/n^2)/(1+1/n^2), right? What's the limit of 1/n and 1/n^2?
 
131
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wait....

the question is (n + 1) / (n^2 +1)

so divide num/denom by n^2 it should be


(n/n^2) + (1/n^2) / (n^2/n^2) + (1/n^2) right?


then it goes

(1/n) + (1/n^2) / 1 + (1/n^2)

then it goes, which is the step I don't understand...


(0+0) / (1 + 0) = 0/1 = 0


where are all these zero's coming from?
 
Dick
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The limit of 1/n as n goes to infinity is zero. Likewise for 1/n^2. The numerator is 1 and the denominator gets larger and larger.
 

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