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

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Homework Help Overview

The discussion revolves around finding the limit of the expression (5h/h(sqrt(25+5h)+5) as h approaches 0, which falls under the subject area of calculus, specifically limits.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various approaches to simplify the limit expression, including canceling terms and using conjugates. Some express uncertainty about their steps and seek clarification on their reasoning.

Discussion Status

The discussion is active, with participants offering guidance on how to manipulate the expression. There is a focus on understanding the correct application of algebraic techniques to evaluate the limit, though no consensus on the final answer has been reached.

Contextual Notes

Participants mention the need to clarify the expression and the steps taken so far, indicating that there may be confusion regarding the setup of the limit problem.

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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...
 
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tcc88 said:
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?
 
Last edited:
footballguy51 said:
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.
 
Or before that cancel out the h on the bottom...
 
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.
 

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