The problem:
If and are positive numbers, prove that the equation
has at least one solution in the interval (-1,1).
I was hoping for some pointers on how to proceed.
Sorry, I made a mistake earlier that was supposed to be a .
The problem:
If and are positive numbers, prove that the equation
has at least one solution in the interval (-1,1).
I was hoping for some pointers on how to proceed.
Sorry, I made a mistake earlier that was supposed to be a .
Hi,
say we write f(x) = .
Then as .
Similarly you can show that as approaches the function value is positive.
Since and are positive numbers, the function "crosses the x-axis" in the interval , and so a solution exists.
I'm sure you can write this in more mathy terms.
Hope this helps!