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Evaluate the limit as y approaches 4

by hunt3rshadow
Tags: approaches, evaluate, limit
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hunt3rshadow
#1
Mar15-12, 04:29 PM
P: 10
1. The problem statement, all variables and given/known data

Evaluate lim y→4

y-3√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.
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scurty
#2
Mar15-12, 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.
Mark44
#3
Mar15-12, 04:37 PM
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P: 21,321
Quote Quote by hunt3rshadow View Post
1. The problem statement, all variables and given/known data

Evaluate lim y→4

y-3√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.
The numerator is quadratic in form, and can be factored.

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.

hunt3rshadow
#4
Mar15-12, 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 factor-able? I dont get what value to factor by.
SammyS
#5
Mar15-12, 04:46 PM
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Quote Quote by hunt3rshadow View Post
1. The problem statement, all variables and given/known data

Evaluate lim y→4

y-3√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.
Of course 4.001 & 3.999 won't give you exactly 1. They give 0.99975 and 1.00025 respectively.
USN2ENG
#6
Mar15-12, 04:47 PM
P: 112
Can you use parenthesis? I can't tell what your sqrt is encompassing.
hunt3rshadow
#7
Mar15-12, 04:50 PM
P: 10
Quote Quote by USN2ENG View Post
Can you use parenthesis? I can't tell what your sqrt is encompassing.
Just the Y. Nothing else.
Mark44
#8
Mar15-12, 04:50 PM
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P: 21,321
Parentheses aren't needed. √y is just the square root of y.
hunt3rshadow
#9
Mar15-12, 04:51 PM
P: 10
Can someone tell me how exactly do I factor the numerator?
Mark44
#10
Mar15-12, 04:53 PM
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P: 21,321
(√y - ?)(√y - ?)

Like that...
Mark44
#11
Mar15-12, 04:54 PM
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P: 21,321
Or if you use my suggestion, you're factoring u2 - 3u + 2.
hunt3rshadow
#12
Mar15-12, 04:59 PM
P: 10
Quote Quote by Mark44 View Post
(√y - ?)(√y - ?)

Like that...
I totally forgot factoring square roots. Thanks. Saved me alotta trouble.


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