Data said:probably safer to assume the limits he wants are
[tex]\lim_{t \rightarrow 9} \frac{9-t}{3-\sqrt{t}}[/tex]
and
[tex]\lim_{x \rightarrow 0} \frac{x^2-81}{\sqrt{x}-3}.[/tex]
The second one is continuous at 0 so you can just sub x=0 in. Are you sure it's not [itex]x \rightarrow 9[/itex] again?
For the first one, you can factor it. I'll let you try for yourself first.
A limit problem is a type of mathematical question that involves finding the value that a function approaches as its input (x) approaches a specific value. It involves evaluating the behavior of a function near a specific point or value.
To solve a limit problem, you can use various techniques such as direct substitution, factoring, rationalization, or L'Hopital's rule. It is also important to understand the properties and rules of limits, such as the limit laws, to correctly solve the problem.
The purpose of using tips and tricks in solving limit problems is to make the process more efficient and to avoid common mistakes. These tips and tricks can also help in understanding the concept better and provide alternative methods for solving the problem.
A one-sided limit is when the input (x) approaches a specific value from only one direction (either from the left or right side), while a two-sided limit is when the input approaches the value from both directions. One-sided limits are used when the function is not defined at a specific point, while two-sided limits are used when the function is defined at the point but may have different values from the left and right side.
No, limit problems can only have one solution. The limit is the value that the function approaches as its input approaches a specific value, and it is unique. However, there can be different methods or approaches to solving the problem, which may result in the same solution.