Solving Limit Probs: x Approaching 0

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In summary, the conversation is about someone asking for help with limit problems. They provide four different limit expressions and mention the use of l'Hopital's rule. They are then reminded to show their attempted workings for better help.
  • #1
celeste6
5
0
hey could anyone help me with some limit probs?
the lim as x approaches 9
(x^2 - 81)/([tex]\sqrt{}x[/tex] - 3)

lim as x approaches 0
(2x+sinx)/x

lim as x approaches o from the right side
(sinx)/(5[tex]\sqrt{}x[/tex])

lim as x approaches 0
(tan7x)/(sin3x)

thanks!
 
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  • #2
You have to show some attempted workings -- not only because doing is the best way to learn, but because then we know where to begin to help. So in this case, are you familiar with l'Hopital's rule?
 
  • #3
ok i'll guess
108
3
?
7/3
 
  • #4
Don't guess! Show us your calculation- it's not that much to want!
 

What is a limit?

A limit is the value that a function approaches as its input approaches a specific value or point. In other words, it is the value that the function "approaches" but may never actually reach.

What is the notation used for limits?

The notation used for limits is "lim" followed by the variable approaching a specific value, followed by the function. For example, if x is approaching 0, the notation would be lim x→0 f(x).

Why is finding the limit as x approaches 0 important?

Finding the limit as x approaches 0 is important because it allows us to understand the behavior of a function near the value of 0. It also helps us to evaluate the continuity and differentiability of a function at a certain point.

How do you solve limit problems as x approaches 0?

To solve limit problems as x approaches 0, you can use algebraic techniques such as factoring, simplifying and rationalizing the expression. You can also use graphical methods or substitution to evaluate the limit.

What are some common mistakes when solving limit problems as x approaches 0?

Some common mistakes when solving limit problems as x approaches 0 include not understanding the concept of a limit, using incorrect notation, and forgetting to check for any potential discontinuities in the function. It is also important to be careful with algebraic manipulations and to always check your work for accuracy.

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