Evaluate the limit as y approaches 4

[hunt3rshadow]

Homework Statement

Evaluate lim y→4

y-3√y + 2
√y - 2

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.

 

[scurty]

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]

Homework Statement

Evaluate lim y→4

y-3√y + 2
√y - 2

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]

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 don't get what value to factor by.

 

[SammyS]

Homework Statement

Evaluate lim y→4

y-3√y + 2
√y - 2

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]

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

 

[hunt3rshadow]

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

Just the Y. Nothing else.

 

[Mark44]

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

 

[hunt3rshadow]

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

 

[Mark44]

(√y - ?)(√y - ?)

Like that...

 

[Mark44]

Or if you use my suggestion, you're factoring u² - 3u + 2.

 

[hunt3rshadow]

(√y - ?)(√y - ?)

Like that...

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