Lizwi said:How do I evaluate this limit I have no Idea, I'm sorry for not showing my work please!
[tex]\lim_{x\to 0}\left(\frac{1}{sin^2x}+\frac{1}{x^2}\right)[/tex]
ME_student said:I have not taken calc yet, but would he need to find a common denominator?
To evaluate a limit, you must first plug in the given value to the function. Then, simplify the expression as much as possible. If you get an indeterminate form, you may need to use algebraic manipulation or one of the limit laws to solve. If the limit still cannot be determined, you may need to use more advanced techniques like L'Hopital's rule or Taylor series.
A limit exists if the left-hand limit and the right-hand limit are equal. This means that the function approaches the same value from both sides of the given value. If these two limits are not equal, then the limit does not exist.
It depends on the limit. If the limit can be evaluated algebraically, then you can use a calculator to help with computations. However, if the limit involves more complex techniques like L'Hopital's rule, then a calculator may not be accurate.
Some common mistakes to avoid are forgetting to check for indeterminate forms, not simplifying the expression enough, and using incorrect limit laws. It is also important to check that the given value is within the domain of the function.
There is no one-size-fits-all shortcut for evaluating limits. However, there are certain techniques and rules that can help simplify the process, such as using the limit laws or recognizing common functions and their limit values. It is important to understand the concept of limits and practice solving various types of limits to become more efficient at evaluating them.