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phymatter
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is limx->infinity xn/ex =0 for n = -ve integers , if yes then why?
also is (->infinity)0 =1 ?
also is (->infinity)0 =1 ?
phymatter said:is limx->infinity xn/ex =0 for n = -ve integers , if yes then why?
also is (->infinity)0 =1 ?
by n = -ve integers i mean that n={-1,-2,-3,-4,...}mathman said:I don't know what you mean by n = -ve integers.
Surely it is not that difficult to write "negative"!phymatter said:is limx->infinity xn/ex =0 for n = -ve integers , if yes then why?
also is (->infinity)0 =1 ?
The notation "Limx->infinity xn/ex =0" is read as "The limit of xn divided by ex as x approaches infinity is equal to 0". It is a mathematical statement used to describe the behavior of a function as the input approaches a very large value (infinity).
This is because, as x approaches infinity, the exponential function ex grows much faster than the polynomial function xn. Therefore, the fraction xn/ex becomes smaller and smaller, eventually approaching 0 as x gets larger and larger.
Yes, it is possible. The limit of xn/ex can be any value other than 0 if the degree of the polynomial xn is greater than or equal to the degree of the exponential function ex. In this case, the exponential function grows slower than the polynomial function, causing the limit to be a non-zero value.
The limit of xn/ex can be used to determine the growth rate of xn and ex. If the limit is 0, it means that the exponential function ex grows faster than the polynomial function xn. If the limit is a non-zero value, it means that the polynomial function xn grows faster than the exponential function ex.
The concept of limits is fundamental in calculus and is used to model various real-world phenomena, such as population growth, radioactive decay, and financial investments. Understanding the limit of xn/ex as x approaches infinity can help in predicting the behavior of these phenomena and making informed decisions.