Question

1、求极限lim（x趋向于3）（2^x —8）\(x—3) 2、求极限lim（x趋向于0）（e^x—e^sinx）\(x

Answer 1

1.lim(x->3) (2^x - 8) / (x-3) o/o型,用洛必达法则

= lim(x->3) 2 ^x * ln2 / 1 = 8 ln2

2.原式 = lim(x->0) e^(sinx) [ e^(x-sinx) - 1 ] / (x - tanx)

= lim(x->0) ( x - sinx) / ( x - tanx) e^(sinx) ->1 ,e^(x - sinx) (x - sinx)

= lim(x->0) ( 1- cosx) / ( 1 - sec²x)

= lim(x->0) (-x²/2) / (- tan²x) = 1/2