Find Limit in 2 Mins - Tricks & Tips

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  • Thread starter Lorena_Santoro
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In summary, the purpose of finding limits in 2 minutes is to quickly and efficiently evaluate the behavior of a function at a particular point. Some tricks for finding limits in 2 minutes include using algebraic manipulation and known limit values or properties. There are also tips for finding limits in 2 minutes, such as practicing and utilizing shortcuts. While it is possible to accurately find limits in 2 minutes, it is important to double check the result and avoid common mistakes such as forgetting one-sided limits and not simplifying the function.
  • #1
Lorena_Santoro
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  • #2
We might recognize the shape of a derivative.
$$\lim_{x\to\infty} x(e^{\frac 1x}-1)
=\lim_{x\to 0} \frac 1x(e^x-1)
=\lim_{x\to 0} \frac{e^x-e^0}{x-0}$$

This is the derivative of $e^x$ at $x=0$, which is $e^0=1$.
 
  • #3
Nice one!
 

FAQ: Find Limit in 2 Mins - Tricks & Tips

1. What is the purpose of finding a limit in 2 minutes?

The purpose of finding a limit in 2 minutes is to quickly and efficiently determine the behavior of a function at a specific point, without having to go through the traditional, more time-consuming methods of calculus.

2. How do I find a limit in 2 minutes?

There are several tricks and tips that can help you find a limit in 2 minutes. These include using the properties of limits, applying L'Hopital's rule, and using known limits of common functions.

3. Can I always find a limit in 2 minutes?

No, not every limit can be found in 2 minutes. Some limits require more complex methods and may take longer to solve. However, many limits encountered in introductory calculus courses can be found in 2 minutes using the aforementioned tricks and tips.

4. What are the benefits of finding a limit in 2 minutes?

The main benefit of finding a limit in 2 minutes is that it saves time and allows for a quicker understanding of the behavior of a function. This can be especially helpful when solving more complex problems that involve multiple limits.

5. Are there any limitations to finding a limit in 2 minutes?

Yes, there are limitations to finding a limit in 2 minutes. As mentioned before, not all limits can be solved in this amount of time. Additionally, finding a limit in 2 minutes may not provide as much insight into the behavior of a function as using traditional methods.

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