Re: A few more GRE questions

In article <4lpVe.236091$5N3.163401@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
N. Silver <mathelp@xxxxxxxxxxxxxxxx> wrote:
>Eric wrote:
>> 1. Which of the following statements are true for every function f,
>> defined on the set of all real numbers, such that lim(x to 0) of f(x)/x
>> is a real number L and f(0)=0?
>> 1. f is differentiable at 0
>> 2. L=0
>> 3. lim (x to 0) f(x)=0
>
>f'(0) = lim[(f(x)-f(0))/(x-0)]. So, the answer is number 1.

Hmmm... I thought it was 3, since

lim f(x) = lim x(f(x)/x) = (lim x)(lim (f(x)/x) = 0L = 0,

which we can do since x is different from 0...

What did I do wrong?

--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================

Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx

.

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