Recent content by 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.

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...

Thank you very much for the help with these questions! Walking me through it helped out a bunch!

Yes that would be 1. So the final answer for making the graph continuous at 0 needs to be 1?

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...