Problem with limits

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FranG

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Nov 23, 2019
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Hello!! Im Fran; I have big problem with this task and I dont know how to solve it!! Please can you help with these complex limit:
Screenshot_1.png
 
I dont understand what Im doing wrong, I just posted task that I cannot solve, litteraly I dont know how to start it! But okay, if you cant help its okay!!
 
FranG said:
I dont understand what Im doing wrong, I just posted task that I cannot solve, litteraly I dont know how to start it! But okay, if you cant help its okay!!
Click to expand...
Have you tried factoring out n^(2/3) from the numerator?
 
FranG said:
Hello!! Im Fran; I have big problem with this task and I dont know how to solve it!! Please can you help with these complex limit:
Click to expand...
It's very helpful when you either show some attempt (even if you know it is wrong), or identify what you find most difficult, or at least tell us what techniques you have learned that you might be able to use. That gives us a place to start.

If it is the presence of n! that makes you afraid to even start, have you noticed that sin(n!) is bounded? Do you see how that helps?
 
FranG said:
Hello!! Im Fran; I have big problem with this task and I dont know how to solve it!! Please can you help with these complex limit:
View attachment 14900
Click to expand...
Because \(\displaystyle \sin(x)\) is a function please use function notation.
Note that if \(\displaystyle n\ge 2\) then \(\displaystyle \sqrt[3]{n^2+2}\cdot\sin(n!)\le (n)^{2/3}\sqrt[3] 2\)
 
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