old question from knowledge plus

2008-01-08 5:40 am

http://www2.hkedcity.net/sch_files/a/kst/kst-06185/public_html/gx.jpg

i don't understand the b part,

why g(0)=f(x)-f(0)/(x-0)= derivative of f(x) ??

in fact, i just don't know why g(0)=f(x)-f(0)/(x-0) .....

is this question so stupid?

.....

更新1:

just ignore my poor handwriting, it is not relevant( some )

回答 (1)

2008-01-08 10:08 am

✔ 最佳答案

g(0)
= lim{x->0} g(x)
= lim{x->0} f(x) / x
= lim{x->0} [f(0+x) - 0] / x
= lim{x->0} [f(0+x) - f(0)] / x
= f'(0)

would this be clearer ??

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