- #1
vbplaya
- 11
- 0
Hey, I just need help with these two statements about limits which happens to be my least favorite topic of calculus. I just need to know if they are true or false and why.
If lim x→c =L, then f(c) = L.
I don't think that is true because f(c) may not always equal L? or is the statement true? I'm not sure
Also:
If f(x) < g(x) for all x≠a, then lim x→a f(x) < lim x→a g(x)
I'm not sure about this one either. I know that if f(x)=g(x) for all x≠c in an open interval containing c, and their limits exists, then lim x→c f(x) = lim x→c g(x). But I don't know if it's is the same for this inequality.
If lim x→c =L, then f(c) = L.
I don't think that is true because f(c) may not always equal L? or is the statement true? I'm not sure
Also:
If f(x) < g(x) for all x≠a, then lim x→a f(x) < lim x→a g(x)
I'm not sure about this one either. I know that if f(x)=g(x) for all x≠c in an open interval containing c, and their limits exists, then lim x→c f(x) = lim x→c g(x). But I don't know if it's is the same for this inequality.