Problem Calculating a limit with a square root, i'm stuck

In summary, the conversation is about solving a limit problem involving a square root. The person is stuck on how to simplify the equation and is seeking help. They attempted to multiply by the conjugate but did not get the correct solution. Ultimately, it is determined that the limit does exist by factoring the numerator.
  • #1
Jordash
64
0
Problem Calculating a limit with a square root, I'm stuck :(

Homework Statement




The limit is equation 9-t / 3-sqrt(t) as t approaches 9

I'm stuck on the how to simplify this?

Thanks for any help.


Homework Equations





The Attempt at a Solution

 
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  • #2


Try multiplying by (3+√t)/(3+√t)
 
  • #3


I discovered that that is the conjugate and I came out with this:

27-6sqrt(t)-tsqrt(t)
----------------
9-t

So in other words, that limit does not exist. Is that right?
 
  • #4


The limit does exist. Instead of multiplying by the conjugate over itself, just factor the numerator, treating it as the difference of two squares.
 

1. How do I calculate a limit with a square root?

To calculate a limit with a square root, you can use the properties of limits and algebraic manipulation. For example, if you have a limit with a square root in the numerator, you can multiply the numerator and denominator by the conjugate of the square root to eliminate the radical. You can also try factoring and simplifying the expression to see if the square root can be cancelled out.

2. What do I do if I'm stuck while trying to calculate a limit with a square root?

If you are stuck while trying to calculate a limit with a square root, try using the graphing calculator or online limit calculator to get a visual representation of the limit. You can also ask for help from a teacher or tutor who can guide you through the problem step by step.

3. Can I use L'Hopital's rule to calculate a limit with a square root?

Yes, you can use L'Hopital's rule to calculate a limit with a square root. However, it is important to note that the rule works best for limits involving fractions or exponential functions. If the limit involves a square root in the denominator, you may need to use other methods such as conjugate or factoring.

4. How do I know if the limit with a square root exists or not?

If the limit with a square root exists, it means that the function approaches a specific value as the input approaches a certain value. You can determine the existence of a limit by evaluating the left and right-hand limits separately and comparing their values. If they are equal, the limit exists. If they are not equal, the limit does not exist.

5. Is there a specific formula for calculating a limit with a square root?

There is no specific formula for calculating a limit with a square root. However, you can use the properties of limits and various algebraic techniques to simplify the expression and evaluate the limit. It is important to have a good understanding of these techniques and practice using them to solve different types of limit problems involving square roots.

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