QuestionFind the left-hand and right-hand limits of as approaches 1, and the limit as approaches -1.
Studdy Solution
STEP 1
Assumptions1. The function is . We are looking for the left-hand limit as approaches1, the right-hand limit as approaches1, and the limit as approaches -1.
STEP 2
First, let's find the left-hand limit as approaches1. This is represented as .
STEP 3
Since the function is continuous everywhere in its domain, the left-hand limit as approaches any value is simply the function evaluated at that value. So, we can substitute into the function to find the left-hand limit.
STEP 4
Now, let's find the right-hand limit as approaches1. This is represented as .
STEP 5
Similarly, since the function is continuous everywhere in its domain, the right-hand limit as approaches any value is simply the function evaluated at that value. So, we can substitute into the function to find the right-hand limit.
STEP 6
Finally, let's find the limit as approaches -1. This is represented as .
STEP 7
Again, since the function is continuous everywhere in its domain, the limit as approaches any value is simply the function evaluated at that value. So, we can substitute into the function to find the limit.
STEP 8
To summarize, the left-hand limit as approaches1 is , the right-hand limit as approaches1 is , and the limit as approaches -1 is .
The exact values of these limits depend on the unit of the angle (radians or degrees) and cannot be simplified further without a calculator.
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