Sunday

January 25, 2015

January 25, 2015

Posted by **Jen** on Sunday, December 3, 2006 at 6:41pm.

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 :)

**Answer this Question**

**Related Questions**

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...

Calculus - Find the limit lim as x approaches (pi/2) e^(tanx) I have the answer ...

calculus - The limit as x approaches infinity of (e^x+x)^(1/x). I got that it ...

Check my CALCULUS work, please! :) - Question 1. lim h->0(sqrt 49+h-7)/h = ...

Calculus - Show that limit as n approaches infinity of (1+x/n)^n=e^x for any x&...

Calculus - Evaluate the following limit. lim e^(tanx) as x approaches the ...

Calculus 3 - Find the limit, if it exists, or show that the limit does not ...

Calculus 3 - Find the limit, if it exists, or show that the limit does not exist...

Calculus - In First principles there is usually a part that states as lim ...

Calculus - Give an example of a function f which is defined at c which limit as ...