Find the Limit of a Challenging Problem: (5h/h(sqrt(25+5h)+5) as h approaches 0

[tcc88]

Can someone help me find the limit of (5h/h(sqrt(25+5h)+5) as h approaches 0? I have tried everything and I can't seem to get an answer [Which is 1/2] other than 0...

 

[footballguy51]

Can someone help me find the limit of (5h/h(sqrt(25+5h)+5) as h approaches 0? I have tried everything and I can't seem to get an answer [Which is 1/2] other than 0...

What kind of work have you done thus far? Show me some of your steps and we can help you understand where your error lies.

$$\lim_{h\to 0} \frac{5h}{h\sqrt{25+5h}+5}$$

Is this the problem you are referring to?

 

[tcc88]

What kind of work have you done thus far? Show me some of your steps and we can help you understand where your error lies.

$$\lim_{h\to 0} \frac{5h}{h\sqrt{25+5h}+5}$$

Is this the problem you are referring to?

Yea, except with quotations separating the h from everything. I am assuming you either have to distribute the h OR multiple the limit by the conjugation.

 

[tcc88]

Or before that cancel out the h on the bottom...

 

[footballguy51]

Okay, so the problem is $$\lim_{h\to 0} \frac{5h}{h(\sqrt{25+5h}+5)}.$$

In that case, this problem isn't too bad. The $h$ in the denominator is multiplied to everything else in the denominator, and so you can cancel it with the $h$ in the numerator. This should help. If I still have the problem wrong, please let me know.