I more than readily admit that some aspects of limits escape me -- I can solve them but my intuitive grasp of them is rusty at best. Where I initially became confused was from seeing "Since limx →0 (1 - (x2/4) = 1". I look at that and think "Hey! They put in 0!"
I'll take a look at that...
@Don:
I'm assuming that the only way 1-(x^2/4) can be equal to 1 is if you assume x=0. I'm also assuming that you have to make x=0 for 1+(x^2/2) equal to 1. Like I said I'm probably grossly misunderstanding some part of this, which is why I'm asking the question. xD From my novice point of view...
This is from a textbook but it is not a homework problem, it's an example following the introduction of the "Sandwich Theorem".
It says "for all x ≠ 0", but then it appears to assume that x = 0 when it finds the limits of g(x) and h(x). Clearly 1 ≤ u(x) ≤ 1 means u(x) = 1, I don't dispute...