First list all the terms out.
e^ix = 1 + ix/1! + (ix)^2/2! + (ix)^3/3! ...
Then, we can expand them.
e^ix = 1 + ix/1! + i^2x^2/2! + i^3x^3/3!...
Then, we can use the rules of raising i to a power.
e^ix = 1 + ix - x^2/2! - ix^3/3!...
Then, we can sort all the real and imaginary terms.
e^ix = (1 - x^2/2!...) + i(x - x^3/3!...)
We can simplify this.
e^ix = cos x + i sin x
This is Euler's Formula.
What happens if we put in pi?
x = pi
e^i*pi = cos(pi) + i sin(pi)
cos(pi) = -1
i sin(pi) = 0
e^i*pi = -1 OR e^i*pi + 1 = 0
That is Euler's identity.
Step-by-step explanation:
2 + x + 2x = 14
3x + 2 = 14 (combine like terms)
3x = 12 (subtract 2 from both sides)
Hence the answer is 3x = 12. (B)
Answer:
Exponentials and logarithms are inverses of each other.
Step-by-step explanation:
Exponentials and logarithms are inverses of each other.
For logarithmic function:
Domain = 
, Range = 
Vertical asymptote is y - axis.
x - intercept is (1,0)
For exponential function:
Domain = , Range =
Horizontal asymptote is x - axis.
y- intercept is (0,1)
Both exponential and logarithmic functions are increasing.
For example:
Solve: 
Answer:
A) 2/15
Step-by-step explanation:
So just divide it normally, do keep change flip
2/3*1/5
2/3 keep
divison change
Denomeinator, flip it, 5 to 1/5
now multiply
2/15
Answer:
you can't find the square root of a negative
Step-by-step explanation:
