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Because Euler proved it! (No, I can't!)
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What is an irrational number less than 0?
Minus square root of 2, minus square root of 3, minus pi, minus e, etc. Or, to be a bit more fancy, 1 - pi, 2 - pi, 3 - pi, pi - 4, pi - 5, 2 - e, e - 3, square root of 2 minus 2, etc.
How do you solve 3e to the power 2x -1 equals 8?
you need to know natural logarithms3e to the 2x-1 power = 8(2x-1) ln e = ln (8/3)ln e = 1(2x-1) = ln(8/3) = 0.982x = 1.98x = 0.99
What is the area bounded by the graph of the function fx equals 1 - e to the power of -x over the interval -1 2?
What is the area bounded by the graph of the function f(x)=1-e^-x over the interval [-1, 2]?
Can an irrational number divided by an irrational number equals an irrational number?
Yes, an irrational number divided by an irrational number will usually be an irrational number, but not always. For example, pi / (3pi) is 1/3, which is a rational number, but pi/e is an irrational number.
What is e to the pi i?
negative one.
How do you manually calculate i to the power of i?
i (taken to be sqrt(-1) for this question) requires that you know a bit about writing complex numbers. i = e^(i*pi/2) so i^i = (e^(i*pi/2))^i which equals e^(i*i*pi/2) since i*i = -1 we get e^(-pi/2) so i^i = e^(-pi/2) which is roughly .207879576
How can you make rational of i power i?
It is NOT rational, but it IS real.Start with Euler's formula: e^ix = cos(x) + i*sin(x) for all x.When x = pi/2,e^(i*pi/2) = cos(pi/2) + i*sin(pi/2) = 0 + i*1 = ior i = e^(i*pi/2)Raising both sides to the power i givesi^i = e^[i*(i*pi/2)] = e^[i*i*pi/2]and since i*i = -1,i^i = e^(-pi/2) = 0.20788, approx.
What is e to the power if i pi?
-1. It is a version of Euler's formula.
Is a power a whole number?
Not necessarily. i times pi is not a whole number, and yet e to the power of i times pi is equal to -1.
What Is The Definition Of Exponential Function In Math?
y = exWhatever your value of x is, you raise e to that power. e is a "transcendental" number like pi, and it equals 2.718281828459045 ...
What is the smallest number such that tan e to power x equals 1?
When x = 3.806663, tan(e^x) = 1.
Which distribution emits a probability density function f x equals 1 over square root of 2 pi times e to the power of minus x squared divided by 2?
That's a Gaussian distribution.
How do you answer E squared times 2 to the 5th power times 3 divided by 6 to the 7th power times 3 minus 4 squared times pi equals 42?
The answer depends on what the question is!
Why is Euler's formula important?
Euler's formula is important because it relates famous constants, such as pi, zero, Euler's number 'e', and an imaginary number 'i' in one equation. The formula is (e raised to the i times pi) plus 1 equals 0.
What mathematical property does e have that pi does not?
Many properties. For example, 1 + 1/1! + 1/2! + 1/3! + 1/4! + ... = e. This is not true for pi.
What did Albert Einstein discover besides E equals mc2?
yes he invented pi
What is e to the power of you times pi?
'e' is an imaginary number, multiplied by anything gives an imaginary result
