- #1
dogma
- 35
- 0
Hi all.
I'm doing some self studying on limits, and...I have the following problem with this problem...
Prove: If [tex]f(x)>0[/tex] for all [tex]x[/tex], then [tex]\lim_{x\rightarrow x_o} f(x)\geq 0[/tex] for any [tex]x_o[/tex]
I'm assuming the best way to prove this is through contradiction:
Assume [tex]\lim_{x\rightarrow x_o} f(x) = A < 0[/tex]
This as far I get before vapor lock sets in. I guess I need to find an appropriate [tex]\epsilon[/tex] and then try to show/not show that [tex]f(x) < 0[/tex] for at least one [tex]x[/tex].
Can someone please point me on the right direction?
Thanks,
dogma
I'm doing some self studying on limits, and...I have the following problem with this problem...
Prove: If [tex]f(x)>0[/tex] for all [tex]x[/tex], then [tex]\lim_{x\rightarrow x_o} f(x)\geq 0[/tex] for any [tex]x_o[/tex]
I'm assuming the best way to prove this is through contradiction:
Assume [tex]\lim_{x\rightarrow x_o} f(x) = A < 0[/tex]
This as far I get before vapor lock sets in. I guess I need to find an appropriate [tex]\epsilon[/tex] and then try to show/not show that [tex]f(x) < 0[/tex] for at least one [tex]x[/tex].
Can someone please point me on the right direction?
Thanks,
dogma