Question

Is there a method to find the outer limit of two functions when trying to find the area between two curves?

Answer 1

upper limit?

Answer 2

Oop sorry. My internet sort of died. So like say i have y = 1/x and y = x^(-3/2). How do I know which one is the upper limit?

Answer 3

Without graphing?

Answer 4

oh upper function?

Answer 5

Yeah. I think.

Answer 6

Do you know how to find the intersections ?

Answer 7

also make note both functions don't exist at x=0

Answer 8

I guess I can do 1/x = x^(-3/2)

Answer 9

yes

Answer 10

\[\frac{1}{x}=\frac{1}{x^{\frac{3}{2}} } \\ x=x^{\frac{3}{2}}\]

Answer 11

How do you flip it?

Answer 12

how do i flip it?

Answer 13

like if 1/a=1/b then a=b
as long a,b isn't 0

or you could multiply both sides by x^(3/2) and x however you like

Answer 14

anyways I find the zeros and were it is undefined
then draw a number line and test intervals around these numbers

Answer 15

you should have found that the equation has a zero at x=1
and both functions are undefined at x=0
also that one with the even root doesn't exist for x<0
so we will only consider our number line for x>0

Answer 16

2 intervals to check

Answer 17

plug in a number between 0 and 1 to see which function is larger on (0,1)
plug in a number after 1 to see which function is larger on (1,inf)