Can this project revolutionize surfing?

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In summary, the conversation revolves around finding the limit of a given function and the steps involved in rationalizing the denominator. The final answer is 1/2. The conversation also touches upon a project being developed that is related to surfing. A link to the project is shared.
  • #1
karush
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find limit $\displaystyle \lim_{x \to 2}\dfrac{\sqrt{6-x}{-2}}{\sqrt{3-x}-1}$
ok I presnume the first thing to do is mulitply by conjugate
 
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  • #2
karush said:
find limit $\displaystyle \lim_{x \to 2}\dfrac{\sqrt{6-x}{-2}}{\sqrt{3-x}-1}$
ok I presnume the first thing to do is mulitply by conjugate
Yes, rationalizing the denominator would be step 1, resulting in

$\displaystyle \lim_{x \to 2} \dfrac{\sqrt{6-x}-2}{2-x} \cdot \lim_{x \to 2} (\sqrt{3-x}+1)$

step 2 would be rationalizing the numerator of the first limit in the product of limitsStep 2 would
 
  • #3
skeeter said:
step 2 would be rationalizing the numerator of the first limit in the product of limits

$\displaystyle \left[ \dfrac{\sqrt{6-x}-2}{2-x}
\cdot \dfrac{\sqrt{6-x}+2}{\sqrt{6-x}+2}
\right]=\frac{\sqrt{-x+3}+1}{\sqrt{-x+6}+2}$
plug in 2
$\dfrac{\sqrt{-2+3}+1}{\sqrt{-2+6}+2}=\dfrac{1}{2}$
hopefully
 
  • #4
karush said:
$\displaystyle \left[ \dfrac{\sqrt{6-x}-2}{2-x}
\cdot \dfrac{\sqrt{6-x}+2}{\sqrt{6-x}+2}
\right]=\frac{\sqrt{-x+3}+1}{\sqrt{-x+6}+2}$

?
 
  • #5
skeeter said:
?
isn't $\dfrac{1}{2}$ the answer
 
  • #6
yes, but that quoted equation you posted is not correct
 
  • #7
$\:\left[\frac{\sqrt{6-x}-2}{2-x}\cdot \frac{\sqrt{6-x}+2}{\sqrt{6-x}+2}\right]:\quad \frac{\sqrt{6-x}-2}{2-x}$

as $x \to 2 $ then $=\dfrac{1}{2}$

however I didn't understand the denominator becoming 0
 
  • #8
$\dfrac{\sqrt{6-x}-2}{2-x} \cdot \dfrac{\sqrt{6-x}+2}{\sqrt{6-x}+2} = \dfrac{(6-x)-4}{(2-x)(\sqrt{6-x}+2)} = \dfrac{\cancel{2-x}}{\cancel{(2-x)}(\sqrt{6-x}+2)} = \dfrac{1}{\sqrt{6-x}+2}$

return to the limit product from post #2

$\displaystyle \lim_{x \to 2} \dfrac{1}{\sqrt{6-x}+2} \cdot \lim_{x \to 2} (\sqrt{3-x}+1)$

$\dfrac{1}{4} \cdot 2 = \dfrac{1}{2}$
 
  • #9
ok I see the calcular was making the 2nd fraction = to 1
...
A project I am developing ,,, its a lot more than I thot

https://dl.orangedox.com/EAwBaH3HAWsQbCDhxF
stn00.png

Surf the Nations back Entry
 
Last edited:

Related to Can this project revolutionize surfing?

1. Can this project really revolutionize surfing?

It is difficult to definitively say whether or not this project will revolutionize surfing, as it ultimately depends on the success and impact of the project. However, the goal of this project is to introduce new technology or techniques that could potentially improve the surfing experience and push the boundaries of the sport.

2. How will this project benefit surfers?

The potential benefits of this project for surfers could include improved performance, increased safety, and enhanced overall experience. By introducing innovative technology or techniques, this project aims to enhance the surfing experience for all levels of surfers.

3. Is this project environmentally friendly?

This project prioritizes sustainability and the protection of the ocean and its ecosystems. Any technology or techniques introduced will be carefully evaluated for their impact on the environment, and efforts will be made to minimize any negative effects.

4. How long will it take for the project to be implemented?

The timeline for implementing this project will vary depending on the specific goals and objectives. It may involve extensive research and development, testing, and collaboration with other experts in the field. The timeline will be determined by the complexity and scope of the project.

5. Will this project be accessible to all surfers?

The goal of this project is to benefit the surfing community as a whole, and efforts will be made to make the technology or techniques accessible to all surfers. However, the accessibility may depend on factors such as cost or location. The project team will strive to make the benefits as widely available as possible.

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