Question9. Calculate the value of the following limit:
Studdy Solution
STEP 1
1. We are dealing with a limit as approaches infinity.
2. The expression inside the limit is a sum of powers of sine functions.
3. We will use properties of limits and the behavior of exponential functions as approaches infinity.
STEP 2
1. Evaluate the sine values.
2. Identify the dominant term as approaches infinity.
3. Apply the limit properties to find the value.
STEP 3
First, evaluate the sine values at the given angles:
STEP 4
Identify the dominant term as approaches infinity. The expression inside the limit is:
Since is the largest value, the term will dominate as .
STEP 5
Apply the limit properties. The dominant term simplifies the expression:
As , the terms and approach 0, leaving:
The value of the limit is:
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