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Is it generally true that limit of e to the power of fx as x tends to infinity is equal to e to the power of limit of fx as x tends to infinity?
YuanHanfb5576
In general, for a continuous function (one that doesn't make sudden jump - the type of functions you normally deal with), the limit of a function (as x tends to some value) is the same as the function of the limit (as x tends to the same value).e to the power x is continuous.
However, you really can't know much about "limit of f(x) as x tends to infinity"; the situation may vary quite a lot, depending on the function. For example, such a limit might not exist in the general case. Two simple examples where this limit does not exist are x squared, and sine of x.
If the limit exists, I would expect the two expressions, in the question, to be equal.
Wiki User
∙ 7y ago
Wiki User
∙ 7y agoYes, provided that the limits exist.
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What is the limit of 2 to the power of infinity?
Infinity.
What is e to the power plus infinity?
infinity
What is e raise power to infinity?
Infinity
What is the domain of y equals 2 raised to the x power?
(-infinity, infinity)
What is when you find the number that when multiplied by the given number they will equal 1?
Anything to the power of 0 is 1, apart from 0 or infinity, because they are just special numbers. :)
What is the limit of 2 to the power of infinity?
Infinity.
What is zero to the fourth power?
Zero to any non-zero real number power is equal to zero. Unless a function evaluates to 'zero to the infinity power' then you must take limits to determine what the limit evaluates to. Zero to the zero power is undefined, but you can take a limit of the underlying function to determine if the limit exists.
What does 2 to the 5555 power equal?
infinity.
Can you use L'hopital's rule for functions?
Yes. The rule is used to find the limit of functions which are an indeterminate form; that is, the limit would involve either 0/0, infinity/infinity, 0 x infinity, 1 to the power of infinity, zero or infinity to the power of zero, or infinity minus infinity. So while it is not used on all functions, it is used for many.
What is infinity to the power infinity?
Also infinity. If you are concerned about the size of sets, it is a higher-level (larger) infinity. For example, 2 to the power aleph-zero, or aleph-zero to the power aleph-zero, is equal to aleph-one.
What is the limit as x approaches infinity of x plus x to the 3rd power plus x to the 5th power all divided by 1 - x to the 2nd power plus x to the 4th power?
Infinity.
Infinity to the power of 1?
Anything to the power of 1 is that same something, so infinity to the power of 1 is infinity. Keep in mind that infinity is a conceptual thing, often expressed as a limit as something approaches a boundary condition of the domain of a function. Without thinking of limits, infinity squared is still infinity, so the normal rules of math would seem to not apply.
What is 2 power to infinity?
If you raise 2 to an infinite power, you get a higher-order infinity. It is still infinity, but a larger number. For example, 2 to the power beth-0 is equal to beth-1; 2 to the power beth-1 is equal to beth-2, etc. Beth-0 is the infinity of counting numbers and integers, beth-1 is the infinity of real numbers, and with beth-2, it gets a bit hard to visualize. Among other things, beth-2 is the infinity of all possible functions over real numbers.
What is e to the power infinity?
E to the power infinity, or lim en as n approaches infinity is infinity.
What is infinity raised to the power infinity?
Infinity.
Is unit impulse an energy signal or power signal?
checking if it is an energy signal E= integration from 0 to infinity of t gives infinity so it is not an energy signal P=limit ( t tending to infinity)*(1/t)*(integration from 0 to t/2 of t) gives us infinity so it is not an energy or a power signal
What is pi to the power of infinity?
Infinity.
