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Evaluate the limit as y approaches 4 
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#1
Mar1512, 04:29 PM

P: 10

1. The problem statement, all variables and given/known data
Evaluate lim y→4 y3√y + 2 √y  2 3. The attempt at a solution If I plug 4 into Y, my answer is undefined. But if I do the chart method, where I plug in 3.999 and 4.0001 the answer is 1. So I'm not quite sure what I'm doing wrong. 


#2
Mar1512, 04:34 PM

P: 392

Try factoring the numerator! The square roots might throw you off a bit, but it's in the same form of a quadratic equation.
You can't plug in 4 directly because the function isn't defined at 4. But limits don't concern themselves with what happens at that point, only what happens very close to that point. 


#3
Mar1512, 04:37 PM

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Or, you can let u = √y, and rewrite the fraction in terms of u, and factor the numerator. With this change, the limit will be as u → 2. 


#4
Mar1512, 04:42 PM

P: 10

Evaluate the limit as y approaches 4
Mark and Scurty, thank you. Mark I get your second method, but for both of you, I don't understand how to factor the numerator. Is it really factorable? I dont get what value to factor by.



#5
Mar1512, 04:46 PM

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#6
Mar1512, 04:47 PM

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Can you use parenthesis? I can't tell what your sqrt is encompassing.



#7
Mar1512, 04:50 PM

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#8
Mar1512, 04:50 PM

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Parentheses aren't needed. √y is just the square root of y.



#9
Mar1512, 04:51 PM

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Can someone tell me how exactly do I factor the numerator?



#10
Mar1512, 04:53 PM

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(√y  ?)(√y  ?)
Like that... 


#11
Mar1512, 04:54 PM

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Or if you use my suggestion, you're factoring u^{2}  3u + 2.



#12
Mar1512, 04:59 PM

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