1. ## [emergency]two Qs about mathematical analysis

These are my bro's questions which are due on Thurs. Advanced thx for any help!

1. the goal of this exercise is to define 2^x from first principle.
Assume that 2^x is already defined when x=a/b is rational(e.g. as the ath power of the bth root of 2 when a,b>0), and that the usual rule 2^(x+y)=2^x * 2^y is valid for rational exponents. Let E(x)={2^r| r belongs to Q, r<x} (a) define 2^x=supE(x) and show that this is finite. (b) prove that 2^(x+y)=2^x * 2^y is valid for real exponents x,y.

2.Using the fundamental theorem of calculus show that (a) the only differentiable functions on R satisfying f'(x)=0, for all x, are constant functions. (b) the only twice differentiable functions on R satisfying f ' '(x)=0 are linear functions i.e function f(x)=ax+b for constant a, b.

2. Originally Posted by elfenlied
These are my bro's questions which are due on Thurs. Advanced thx for any help!

1. the goal of this exercise is to define 2^x from first principle.
Assume that 2^x is already defined when x=a/b is rational(e.g. as the ath power of the bth root of 2 when a,b>0), and that the usual rule 2^(x+y)=2^x * 2^y is valid for rational exponents. Let E(x)={2^r| r belongs to Q, r<x} (a) define 2^x=supE(x) and show that this is finite. (b) prove that 2^(x+y)=2^x * 2^y is valid for real exponents x,y.

2.Using the fundamental theorem of calculus show that (a) the only differentiable functions on R satisfying f'(x)=0, for all x, are constant functions. (b) the only twice differentiable functions on R satisfying f ' '(x)=0 are linear functions i.e function f(x)=ax+b for constant a, b.
Who's problems are they? Yours?
So what have you done to solve them?
How can we help if we don't know that?

BTW: This is not a homework service. It is a HELP site.

3. Originally Posted by Plato
Who's problems are they? Yours?
So what have you done to solve them?
How can we help if we don't know that?

BTW: This is not a homework service. It is a HELP site.
they are my brother's Qs. im majored on CS rather than Math, so i can do nothing about these Qs. My brother just doesnt know where to start.

4. Originally Posted by elfenlied
they are my brother's Qs. im majored on CS rather than Math, so i can do nothing about these Qs. My brother just doesnt know where to start.
So let your brother do his own posting.
Why are you even involved?