calculus again
posted by Jen .
Suppose lim x>0 {g(x)g(0)} / x = 1.
It follows necesarily that
a. g is not defined at x=0
b. the limit of g(x) as x approaches equals 1
c.g is not continuous at x=0
d.g'(0) = 1
The answer is d, can someone please explain how?
Thanks.
lim x>0 {g(x)g(0)} / x = 1.
You can use the definition of the derivative:
g'(x) = Lim h> [g(x+h)  g(x)]/h
Take x = 0:
g'(0) = Lim h> [g(h)  g(0)]/h
And h is just a "dummy variable" whose name doesn't matter :)
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