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.
Question: Guess the oblique asymptote of the graph f(x) for x→∞. Write down the limit you have to compute to prove that your guess is correct.
f(x)= \sqrt{(x^{4}+1)/(x^{2}-1)}
so the limit would be: lim x→∞ \sqrt{(x^{4}+1)/(x^{2}-1)}
I sketched out a graph but I just have no clue how to...
f(c)=0 and if you were to replace that into the equation for f(x) you would get f(x)=e^{-0^{2}} which would end up equaling 1, right?
Sorry about this, all of this is really new to me so it's tough to grasp at first.
Ahh so it would be 0 because e^{-∞} is extremely small.
It means that f(x)=f(c) as x→c. So basically that the function can be drawn without having to lift the pen to complete the graph.
So, e^{-∞^{2}} would be approaching -∞?
I have 2 questions in regards to continuity and limits.
Question 1:
f(x)= e^{-x^{2}} if x ≠ 0.
f(x)= c if x=0.
For which value of c is f(x) continuous at x=0?
I was thinking the answer would be 1 but I feel that's incorrect.
Question 2:
Compute lim x→∞f(x).
I'm not familiar with how to...