N is an integer. Write the values of n such that -15 < 3n <6 I need know please
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Answer:
The area of the searched region is
Step-by-step explanation:
If you want to find the area of a region bounded by functions f(x) and G(x) between two limits (a,b), you have to do a double integral. you must first know which of the functions is greater than the other for the entire domain.
In this case, for 0<x<1, f(x)<g(x)
while for 1<x, g(x)<f(x).
Therefore if our domain is all real numbers superior to 0 (where the limit 0<a<1 and 1<b), we have to do 2 integrals:
A=A(a<x<1)+A(1<x<b)
[scomposition of 45]
[9 = 3^2, must use this notation (not 3*3)]
[We appy one of the proprieties of square roots]
[now we semplify: we must take out as much as possible all the elements under roots]
[to do that, we must divide the esponent of each element with the index of square roots (2)]
so
, 2/2 = 1
, 1/2 = 0 with 1 of rest
, 5/2 = 2 with 1 rest
[well, after do that, we can take out the elements under tbhe square roots!]
The quotient of each division is the esponent of the element out of the root
The rest of each division is the esponent of the element under the root
so:
(quotient = 1, see the first operation) *
(rest = 1, see the second operation) *
(quotient = 2, see the third operation) *
(rest = 1, see the third operation)
The final result is:
3 (=3^1) * a² * √5 * √a
3a²√5a
It's more intuitive and easy, but the explanation (necessary) is very long. If you have other questions, ask me here in the comments! Also sorry for my english, not so good!