Solve Limit Problem: SQRT(-2)/(4-x) as x Approaches 4

[Niaboc67]

Homework Statement

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Determine if the limit exists as a number, ∞, -∞ or DNE
lim x->4^- -(2)/(sqrt(4-x))

The Attempt at a Solution

lim x->4^-...

I honestly don't know how to solve. Because I don't know what to do with the sqrt function. If someone could lead me in the right direction here that would be great.
Thank you

 

[Mark44]

Homework Statement

Determine if the limit exists as a number, ∞, -∞ or DNE
lim x->4^- -(2)/(sqrt(4-x))

The Attempt at a Solution

lim x->4^-...

I honestly don't know how to solve. Because I don't know what to do with the sqrt function. If someone could lead me in the right direction here that would be great.
Thank you

This is actually pretty straightforward. The numerator doesn't change. What happens to the denominator as x gets closer to 4 from the left?

 

[Niaboc67]

Looks like it's getting smaller and smaller from this graph I am looking at for 1/sqrt(x)?

 

[Mark44]

Looks like it's getting smaller and smaller from this graph I am looking at for 1/sqrt(x)?

Can you be more specific? x is approaching 4 from the left.
What is the overall fraction doing?

 

[Niaboc67]

I solved it. It was lim as x approaches 4 from the negative side. so I put it must be something like -2/sqrt(4-3.9999) so inf digits and therefore, -inf

 

[verty]

I solved it. It was lim as x approaches 4 from the negative side. so I put it must be something like -2/sqrt(4-3.9999) so inf digits and therefore, -inf

Yes and that is exactly how you want to think about it.