Analysis: Find limits

  • #1
1,654
2
1) = 0

The denominator grows much faster than the numerator.

2) = 0

Each of these terms would simply be zero, right?

For 4) and 5), the f(x) = x3

I simplified these to

4) = [(x-2)(x2+2x+4)]/(x-3)

5) = [(x-3)(x2+3x+9)]/(x-2)

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled2.png [Broken]

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled.png
 
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Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
956
1) = 0

The denominator grows much faster than the numerator.

2) = 0

Each of these terms would simply be zero, right?
(1) is correct, (2) is not. In (2) your sequence is
[tex]\frac{1}{n}+ \frac{2}{n}+ \cdot\cdot\cdot+ \frac{n}{n^2}= \frac{1+ 2+ 3+ \cdot\cdot\cdot+ n}{n^2}[/tex]

Use the fact that [itex]1+ 2+ 3+ \cdot\cdot\cdot+ n= (1/2)n(n+1)[/itex].

If you are thinking you can take the limit in each term so that you get 0 for each, no that is not correct.

For 4) and 5), the f(x) = x3

I simplified these to

4) = [(x-2)(x2+2x+4)]/(x-3)
You can do that but the obvious point should be that denominator goes to 0 while the numerator goes to f(3)- f(2)= 27- 8 which is NOT 0.

5) = [(x-3)(x2+3x+9)]/(x-2)
Again, the denominator goes to 0 while the numerator does not.

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled2.png [Broken]

http://i111.photobucket.com/albums/n149/camarolt4z28/Untitled.png
 
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  • #3
1,654
2
For 2), I didn't know you could rewrite the sum in that manner.

I then get [(1/2)n(n+1)]/n = (1/2)[(n+1)/n] = 1/2.

If I had to guess, I would say 4) and 5) go to +/- infinity, respectively.
 
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  • #4
1,654
2
Am I right?
 

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