祈求数学高手解答,大学
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f(x)
=x^2.sin(1/x) + sin2x ; x≠0
=0 ; x=0
lim(x->0) f(x)
=lim(x->0) [x^2.sin(1/x) + sin2x ]
=0
=f(0)
x=0, f(x)连续
f'(0)
=lim(h->0) [h^2.sin(1/h) + sin2h -f(0)]/h
=lim(h->0) [h^2.sin(1/h) + 2h]/h
=lim(h->0) [h.sin(1/h) + 2]
=2
ie
f'(0)=2
