Hi, im taking my first analysis course and we are studying Limits right now. My prof said they are the most important thing to remember out of this whole semester. Anyways i have two problems im trying to solve that i could do with some help.(adsbygoogle = window.adsbygoogle || []).push({});

1) Show that if [tex]f(x) \leq 0[/tex] and [tex]\lim_{x->a} f(x) = l[/tex], then [tex]l \leq 0[/tex].

2) If [tex]f(x) \leq g(x)[/tex] for all x, then [tex]\lim_{x->a} f(x) \leq \lim_{x->a} g(x)[/tex].

If those limits exist.

For number one i can see this is obvious but i don't know where to start to try and prove it.

I know the definitions for limits, do i use them somehow?

For number 1) i think that i can use a proof by contradiction somehow.

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# Analysis Proof Help :S

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