一.definition and theorem
1. average rate of change
2.THEOREM 1—Limit Laws
3.THEOREM 2—Limits of Polynomials
4.THEOREM 3—Limits of Rational Functions
5.THEOREM 4—The Sandwich Theorem
Suppose that g ( x ) ≤ f ( x ) ≤ h ( x ) g(x) \leq f(x)\leq h(x) g(x)≤f(x)≤h(x) for all x in some open interval containing c, except possibly at x = c itself. Suppose also that lim x → c g ( x ) = lim x → c h ( x ) = L \lim_{ x\rightarrow c }g(x)=\lim_{x\rightarrow c}h(x)=L x→climg(x)=x→climh(x)=L
then
lim x → c f ( x ) = L \lim_{ x\rightarrow c }f(x)=L x→climf(x)=L
5.THEOREM 5
If f ( x ) ≤ g ( x ) f(x)\leq g(x) f(x)≤g(x)for all x in some open interval containing c,except possibly at x = c itself, and the limits of ƒ and g both exist as x approaches c,then lim x → c f ( x ) ≤ lim x → c g ( x ) \lim_{x\rightarrow c}f(x)\leq \lim_{x\rightarrow c}g(x) x→climf(x)≤x→climg(x)
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