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f(x) given below, evaluate
{:[lim_(x rarr oo)f(x)" and "lim_(x rarr-oo)f(x).],[quad f(x)=5sin(4x^(3))]:}](https://blblobstorage.blob.core.windows.net/solver-b2c/2344c9c4-00cd-11ef-9921-fae99310ca6d.jpg)
For the function given below, evaluate
Full solution
Q. For the function given below, evaluate
- Consider sine function behavior: To find the limit as approaches infinity, we need to consider the behavior of the sine function. The sine function oscillates between and , no matter how large gets.
- Behavior of : Since will become very large as approaches infinity, the argument of the sine function will also become very large. This means the sine function will keep oscillating.
- Limit as approaches infinity: Because the sine function oscillates and doesn't approach a single value, the limit of as approaches infinity does not exist.
- Behavior as approaches negative infinity: Similarly, as approaches negative infinity, will become very large in the negative direction, and the sine function will continue to oscillate between and .
- Conclusion: Therefore, the limit of as approaches negative infinity also does not exist.
