Limit as x approaches infinity, involves sinx and cosx

In summary, the limit as x approaches infinity refers to the behavior of a function as the input value (x) gets larger and larger. Sinx and cosx are commonly used in these types of limits to describe the behavior of the function. Multiple solutions can exist for a limit involving sinx and cosx due to their periodic nature. The main difference between a limit as x approaches infinity and a limit as x approaches a specific value is the value that x is approaching. To determine the limit as x approaches infinity for a function involving both sinx and cosx, you can use trigonometric properties and the rules of limits, as well as graphing tools for visualization.
  • #1
rygza
38
0
y=1/2(sinx-cosx+e(^pi-x))

question: if x approaches infinity, which term or terms will dominate?
from my understanding, sinx and cosx will oscillate and the e term will approach zero. so would the answer be sinx-cosx?

please and ty
 
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  • #2
since the e^(pi-x) term approaches 0, it has no real impact on the sin x and cos x terms. the oscillating terms mean that the limit DNE, not that the limit is sin x-cos x (answer should not be in terms of x, anyway)
 

FAQ: Limit as x approaches infinity, involves sinx and cosx

1. What does "limit as x approaches infinity" mean?

The limit as x approaches infinity refers to the behavior of a function as the input value (x) gets larger and larger. In other words, it describes what happens to the output of the function as x gets closer and closer to infinity.

2. How is sinx and cosx involved in limits as x approaches infinity?

Sinx and cosx are trigonometric functions that are commonly used in limits as x approaches infinity. These functions can be used to describe the behavior of a function as x gets larger and larger, and can help determine the limit of the function as x approaches infinity.

3. Can a limit as x approaches infinity involving sinx and cosx have multiple solutions?

Yes, a limit as x approaches infinity involving sinx and cosx can have multiple solutions. This is because these functions have periodic behavior, meaning they repeat themselves after a certain interval. As a result, there may be multiple values of x that result in the same limit as x approaches infinity.

4. What is the difference between a limit as x approaches infinity and a limit as x approaches a specific value?

The main difference between these two types of limits is the value that x is approaching. In a limit as x approaches infinity, x is getting larger and larger without any specific endpoint. In a limit as x approaches a specific value, x is getting closer and closer to a specific number.

5. How can I determine the limit as x approaches infinity for a function involving both sinx and cosx?

To determine the limit as x approaches infinity for a function involving both sinx and cosx, you can use the properties of these trigonometric functions and the rules of limits. This may involve simplifying the function or using trigonometric identities to rewrite it in a more manageable form. You can also use a graphing calculator or software to visualize the behavior of the function as x approaches infinity.

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