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gipc
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How do I formally show that lim x^2 - sin(x) as x tends to infinity is infinity?
The limit of a function at a certain point is the value that the function approaches as the input approaches that point.
To calculate a limit, you must evaluate the function at values closer and closer to the point in question, and see what value the function is approaching.
To show that a limit is approaching infinity, you must show that the function is growing without bound as the input approaches the point in question. In the case of the function x^2-sin(x), as x approaches infinity, the value of the function will also approach infinity.
The step-by-step process for calculating this limit is as follows:
1. Plug in larger and larger values for x, such as 100, 1000, 10000, etc.
2. Observe that as x gets larger, the value of the function also gets larger.
3. This indicates that the limit is approaching infinity.
Yes, a graph can be used to show that the limit of x^2-sin(x) as x approaches infinity is infinity. If you plot the function on a graph, you will see that as x approaches infinity, the graph will continue to rise without bound, indicating that the limit is infinity.