- #1
daster
I'm having trouble with limits that involve 0+ and 0-. Can someone show me how the answers to the following limits are obtained?
[tex]f(x) = \frac{1}{1+e^{\frac{1}{x}}}[/tex]
[tex]\lim_{x\rightarrow0^{+}} = 0[/tex]
[tex]\lim_{x\rightarrow0^{-}} = 1[/tex]
Now, my second query involves continuity. I understand that:
[tex]f(x) \in C \Leftrightarrow \lim_{x \rightarrow a} f(x) = f(a)[/tex]
Say we have:
[tex]f(x) = \frac{\sin x}{x}[/tex]
Is f(x) continuous at x=0? My book says it is if f(0) is defined as 1. What am I missing?
Finally, what exactly is Cn?
[tex]f(x) = \frac{1}{1+e^{\frac{1}{x}}}[/tex]
[tex]\lim_{x\rightarrow0^{+}} = 0[/tex]
[tex]\lim_{x\rightarrow0^{-}} = 1[/tex]
Now, my second query involves continuity. I understand that:
[tex]f(x) \in C \Leftrightarrow \lim_{x \rightarrow a} f(x) = f(a)[/tex]
Say we have:
[tex]f(x) = \frac{\sin x}{x}[/tex]
Is f(x) continuous at x=0? My book says it is if f(0) is defined as 1. What am I missing?
Finally, what exactly is Cn?