推 GayerDior:謝謝你~~~~(￣▽￣)~(＿△＿)~(￣▽￣)~ 61.229.155.78 07/16 16:03
※ 引述《GayerDior ( ~(￣▽￣)~)》之銘言：
: [成功大學]
: Let f(x) be differentiable for x>0. Prove or disprove
: (1)If lim f(x)=0. then lim f'(x)=0.
: x->oo x->oo
f(x) = sin(x^2)/x -> 0 as x -> oo
f'(x) = 2cos(x^2) - sin(x^2)/x^2
lim f'(x) fails to exist
x->oo
: (2)If lim lim
: + f(x)=oo. then + f'(x)=-oo
: x->0 x->0
: 如果有人會寫，請幫我寫出詳細過程，
: 謝謝。
f(x) = 1/(x^2)[sin(1/x)+2] -> oo as x -> 0+
f'(x) = -{2x[sin(1/x)+2] - cos(1/x)}/{(x^2)[sin(1/x)+2]}^2
lim f'(x) fails to exist
x->0+
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※ 編輯: SMer 來自: 61.223.41.99 (07/16 13:42)