# Limit Calculation with Multiplication Trick?

• gipc
In summary, the conversation is about solving a limit using L'Hôpital's rule, but there is also another way to solve it by multiplying the numerator and denominator by (sqrt(x)+sqrt(a)). However, it is noted that the two-sided limit does not exist. Further discussion is had about the proper way to multiply the terms.
gipc
Hello,

can someone please help me understand how to solve the following limit? I've tried multiplying by sqrt(x)+sqrt(a) but it doesn't seem to do the trick. How do i continue from there?

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L'Hôpital's rule does the job here, check http://en.wikipedia.org/wiki/L'Hôpital's_rule , but as I'm not such a fan of L'Hôpital there is usually a way to work yourself around hopital but I don't see it at this moment. Again, use L'Hôpital for an easy way out here!

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gipc said:
Hello,

can someone please help me understand how to solve the following limit? I've tried multiplying by sqrt(x)+sqrt(a) but it doesn't seem to do the trick. How do i continue from there?

The[/URL] two-sided limit doesn't exist, because if x < a, then the denominator is not a real number. The right-side limit exists, though. If you assume that x > a, multiplying numerator and denominator by sqrt(x) + sqrt(a) will get you something that you can evaluate.

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Ah, took me a while but you should rather multiply nominator and denominator $$(x^{\frac{1}{2}}+a^{\frac{1}{2}})(x+a)$$ so you can REALLY evaluate the limit with ease :)

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I repeat - the two-sided limit doesn't exist, so if you get a value for it, your work is wrong.

justsof said:
Ah, took me a while but you should rather multiply nominator and denominator $$x^{\frac{3}{2}}+a^{\frac{3}{2}}$$ so you can REALLY evaluate the limit with ease :)
And how does that work? Are you saying that (x1/2 - a1/2)(x3/2 + a3/2) gives you something easy to work with? The middle terms do not drop out.

You are right, sorry, I meant multiplying by (x+a)(sqrt(x)+sqrt(a)) but didn't think it over.

## 1. What is a limit in mathematics?

A limit in mathematics is a fundamental concept that refers to the value that a function approaches as the input approaches a certain value. It represents the behavior of a function near a particular point.

## 2. How do you calculate a basic limit?

To calculate a basic limit, you first need to substitute the value of the input into the function. Then, you simplify the resulting expression as much as possible. Finally, you evaluate the expression to find the limit.

## 3. What is the difference between a one-sided and two-sided limit?

A one-sided limit only considers the behavior of the function on one side of the input value, while a two-sided limit considers the behavior on both sides of the input value.

## 4. When is a limit undefined?

A limit is undefined when the function does not approach a specific value as the input approaches a certain value. This can happen when there is a discontinuity or a vertical asymptote in the function.

## 5. Why is finding limits important in mathematics?

Finding limits is important in mathematics because it helps us understand the behavior of a function and make predictions about its values. Limits also play a crucial role in calculus, which is used in various fields such as physics, economics, and engineering.

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