I think I'll proceed to slapping myselfJonathan Scott said:That would be the answer if that wasn't a cube root but a badly formatted ##3 \sqrt{t}##.
Arnoldjavs3 said:I think I'll proceed to slapping myself
A limit is the value that a function approaches as the input (usually denoted by x) gets closer and closer to a particular value (usually denoted by a). It is like finding the value of a function at a specific point without actually plugging in that point.
Simplifying the expression helps us to better understand the behavior of the function and to find the limit more easily. It also allows us to use algebraic techniques to solve the limit, rather than relying on graphing or numerical methods.
To simplify a limit with squareroot, you can use algebraic techniques such as factoring, rationalizing the denominator, or using the conjugate. It is important to keep in mind any restrictions on the domain of the function and to simplify as much as possible before plugging in the value of x.
Not always. Sometimes, the limit may not exist or may be undefined, in which case simplifying will not be possible. Additionally, there may be limits that require more advanced techniques, such as L'Hopital's rule, to solve.
If you have simplified correctly, the simplified expression should be equivalent to the original expression in terms of its behavior and values at different points. You can also check your answer by graphing the original and simplified expressions and seeing if they match.