Let g be a function that is differentiable throughout an

Chapter , Problem 6AAE

(choose chapter or problem)

Let \(g\) be a function that is differentiable throughout an open interval containing the origin. Suppose \(g\) has the following properties:

i. \(g(x+y)=\frac{g(x)+g(y)}{1-g(x) g(v)}\) for all real numbers \(x, y\),  and \(x + y\) in the domain \(g\).

ii. \(\lim _{h \rightarrow 0} g(h)=0\)

iii. \(\lim \limits_{h \rightarrow 0} \frac{g(h)}{h}=1\)

a. Show that \(g(0)=0\) .

b. Show that \(g^{\prime}(\mathrm{x})=1+[g(\mathrm{x})]^{2}\).

c. Find \(g(\mathrm{x})\) by solving the differential equation in part (b).

Equation Transcription:

Text Transcription:

g(x+y) = g(x) + g(y) / 1 - g(x)g(y)

x, y and x+y

g

lim_h right arrow 0 g(h) = 0

lim_h right arrow 0 g(h) /h = 1

g(0) = 0

g^prime (x) = 1 + [g (x)]^2

g (x)

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Becoming a subscriber
Or look for another answer

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back