Limits question involving trigonometric functions

[dustinm]

f(x)= ((cosx)$^{2}$+1)/e$^{x}$$^{2}$

So for the limit of f(x) as x→∞ I would just input ∞ for x. I'm confused after this though, wouldn't it just be ∞/∞ = 1?

the next part says show that there exists a number c ε (0,1) that f(c)=1
I don't know what this is asking for me to solve.

 

[SammyS]

f(x)= ((cosx)$^{2}$+1)/e$^{x}$$^{2}$

So for the limit of f(x) as x→∞ I would just input ∞ for x. I'm confused after this though, wouldn't it just be ∞/∞ = 1?

What is the maximum value of (cos(x))²? the minimum value of (cos(x))²?

the next part says show that there exists a number c ε (0,1) that f(c)=1
I don't know what this is asking for me to solve.

What is f(0) ?

What is f(1)?