Recent content by gaborfk

Can you be a little bit more specific please? Thank you

Homework Statement Prove that if f''(x) exists and is continuous in some neighborhood of a, than we can write f''(a)= \lim_{\substack{h\rightarrow 0}}\frac{f(a+h)- 2f(a)+f(a-h)}{h^2} The Attempt at a Solution I just proved in the first part of the question, not posted, that...

Never mind... Just did g'(0) and plug in...

Solved: Real Analysis, differentiation Homework Statement If g is differentiable and g(x+y)=g(x)(g(y) find g(0) and show g'(x)=g'(0)g(x) The Attempt at a Solution I solved g(0)=1 and I got as far as g'(x)=\lim_{\substack{x\rightarrow 0}}g(x) \frac{g(h)-1}{h} but now I...

Homework Statement Using a delta epsilon method prove: \mathop {\lim }\limits_{x \to 1 } x^3+2x^2-3x+4= 4 The Attempt at a Solution I got so far as breaking the equation into =|x||x+3||x-1| now how do I bound it? Also, even more basic question, once I found the bound how do I put the...

Because there are infinitely many irrational numbers which would make the graph continuous on the irrationals, but on an interval there would be rationals mixed in between the irrationals?

Thank you! That sound great.

Homework Statement For each a\in\mathbb{R}, find a function f that is continuous at x=a but discontinuous at all other points. The Attempt at a Solution I guess I am not getting the question. I need to come up with a function, I was thinking of a piecewise defined one, half rational...

I know that the function is continuous at x=0. So how does showing it is continuous at zero help with showing the function with the property f(x_{1}+x_{2})=f(x_{1})+f(x_{2}) is continuous? Thank you

Homework Statement Prove: If f is defined on \mathbb{R} and continuous at x=0, and if f(x_{1}+x_{2})=f(x_{1})+f(x_{2}) \forall x_{1},x_{2} \in\mathbb{R}, then f is continuous at all x\in\mathbb{R}. Homework Equations None The Attempt at a Solution Need a pointer to get started...

Homework Statement Describe the locus of points z satisfying the given equation. Homework Equations Im(2iz)=7 |z-i|=Re(z) The Attempt at a Solution I started on the second one: I think that Re(z) is just x, then I squared both sides, simplified and got (y-1)^2=0 is this...

Thank you! The "hard ones" are so easy sometimes...

You mean that if \int \limits_a^b f(x) dx=0 and \int \limits_a^b g(x) dx=0, can I prove that \int \limits_a^b f(x)+g(x) dx=0? Also, if \int \limits_a^b f(x) dx=0 then k\int \limits_a^b f(x) dx=0?

Definition of subspace means that the functions are closed under addition and scalar multiplication

Yet another problem I need to get some starting help on: Show that the set of continuous functions f=f(x) on [a,b] such that \int \limits_a^b f(x) dx=0 is a subspace of C[a,b] Thank you