QuestionEvaluate the limit or state if it doesn't exist: (3 decimal places or DNE)
Studdy Solution
STEP 1
Assumptions1. We are trying to find the limit of the function as approaches . . We are using the standard limit properties and the known limit .
STEP 2
The problem is that we cannot directly substitute into the function, because it would result in a form of , which is undefined. However, we can use the known limit to help us.
STEP 3
To use the known limit, we need to make the function in the form of . We can do this by multiplying and dividing the function by .
STEP 4
Now, we can see that the function is in the form of , where is replaced by . According to the limit properties, if we have a constant multiple inside a limit, we can take it outside of the limit.
STEP 5
Now, we can use the known limit to evaluate the limit.
STEP 6
Calculate the final value.
So, the limit of the function as approaches is .
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