Suppose limit as x approaches 0 is (g(x)-g(0))/x =1. What would be true?

Question

turingtest · Answer

a lot, but I'm guessing they want you to recognize that$$g'(a)=\lim_{x\to a}{f(x)-f(a)\over x-a}$$

turingtest · Answer

those should all be g's not f's

turingtest · Answer

$$g'(a)=\lim_{x\to a}{g(x)-g(a)\over x-a}$$use this fact to answer the question

anonymous · Answer

yes. But my choices are A. g is not defined at x=0 B. g is not continous at x=0 C. The limit of g(x) as x approaches 0 =1 D. g'(0)=1 g'(1)=0

asnaseer · Answer

for the limit to exist at x=0, g must be continuous at x=0

turingtest · Answer

great, so using the information I gave you and decide which choice is correct.

asnaseer · Answer

TuringTest is correct - follow his lead

anonymous · Answer

I don't really understand. Could you explain it a little diferently please?

anonymous · Answer

But I do know that I've seen the formula before.

asnaseer · Answer

the formula given by TuringTest is the definition of a derivative

anonymous · Answer

So I believe that my answer is C, because it is telling what is happening in words

asnaseer · Answer

not quite - the question does not say "the limit as x approaches zero of g(x) = 1"

anonymous · Answer

Since that was the formula for for derivative g'(0)=1would be true?