11=11=!1=11...=1
Infinity
the answer is e raise to power minus pi/2
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.
10 (or e) to the power of x range from zero to infinity. Lets try the extreme cases: 10^infinity = infinity 10^0 = 1 10^-infinity = 1/infinity = 0
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.
E to the power infinity, or lim en as n approaches infinity is infinity.
The value of anything raised to the power of infinity depends on the base. If the base is greater than 1, the value approaches infinity. If the base is equal to 1, the value remains 1. If the base is between 0 and 1, the value approaches 0. If the base is 0, the expression is typically considered to be 0, but if it's 0 raised to the power of infinity, it is an indeterminate form.
Infinity.
Infinity.
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.
Infinity.
If you raise the number 1 to ANY power, you get 1.