- #1
ayandas
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Hi,
Can anyone please suggest a solution to the problem:
lim 10n/(n!)
n->(infinite)
Can anyone please suggest a solution to the problem:
lim 10n/(n!)
n->(infinite)
The limit of 10^n/n as n approaches infinity approaches infinity. This means that the value of the limit will continue to increase without bound as n gets larger and larger.
To prove that the limit of 10^n/n as n approaches infinity is infinity, we can use the definition of a limit. We need to show that for any arbitrarily large number M, there exists a corresponding value of n where 10^n/n is greater than M. This can be done by manipulating the expression 10^n/n to show that it can be made arbitrarily large as n increases.
No, the limit of 10^n/n as n approaches infinity cannot approach a finite number. This is because the expression 10^n/n will continue to increase without bound as n gets larger, meaning it will never approach a fixed value.
If we replace 10 with a different number in the expression 10^n/n as n approaches infinity, the limit will still approach infinity. This is because any number raised to a large enough power will eventually become larger than n, causing the expression to increase without bound.
Yes, the concept of limits is widely used in scientific research, including in fields such as calculus, physics, and economics. The limit of 10^n/n as n approaches infinity is particularly useful in understanding the behavior of exponential growth and can be applied to various real-world scenarios.