Limits

We are given the limit expression: To evaluate this limit, we analyze the behavior of the numerator and denominator as :
- The terms and grow exponentially as increases, while the terms involving and constants become insignificant in comparison.
Hence, the dominant term in the numerator will be .
- In the denominator, is bounded, since oscillates between -1 and 1.
Therefore, the denominator remains finite. Since the numerator grows exponentially, while the denominator stays bounded, the limit of the expression as will tend to infinity:
Thus, the value of the limit is .