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Evaluate: lim (1+h)^4-1/ h h->0
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exapand it again :)
1+h 1+h ---- 1 +h +h +h^2 ----------- 1 +2h +h^2 1 +2h +h^2 1 +2h +h^2 ----------- 1 +2h +h^2 +2h +4h^2 +2h^3 +h^2 +2h^3 +h^4 ------------------------ 1 +4h +6h^2 +4h^3 +h^4 1 +4h +6h^2 +4h^3 +h^4 -1 --------------------------- h
holy crap
anything left with an 'h' in it goes under; which means we are left with 4 in the end
4h +6h^2 +4h^3 +h^4 --------------------- h h h h 4 +6h +4h^2 +h^3 ; when h=0 , this = 4
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