Question

设x→0,limf(x)/x=0,f''(0)=4,证明:x→0,limf(x)/x^2=2

Answer 1

x→0

因为f''(0)=4,故,f'(x)在x=0处连续

而

lim f(x)/x极限存在,故该极限必为0/0型,利用L'Hospital法则

=lim f'(x)

=f'(0)

=0

lim f(x)/x^2

该极限为0/0型,利用L'Hospital法则,

=lim f'(x)/2x

该极限为0/0型,利用L'Hospital法则,

=lim f''(x)/2

=f''(0)/2

=4/2

=2

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