Recent content by rapple

This is in real analysis in the section on exponential functions. So I can't use differential equations. The only way, I suppose, is to arrive at a contradiction if c not= f(0).

Homework Statement f(x)=f'(x) for all x in R S.T there exists a c in R such that f(x) = c exp(x) for all x Homework Equations The Attempt at a Solution By defining g = f/c, I was able to show that c= f(0) But i am also supposed to show that c Not equal to any other value I...

Since lim n->inf (1/n)=0, as n-> infinity, f_n(x) will be 0 for rationals as well. which means that for any epsilon>0, if n is large enough, |f(x)-0|< epsilon for rational as well?

Homework Statement Need an example of a sequence of functions that is discountinuous at every point on [0,1] but converges uniformly to a function that is continuous at every point Homework Equations The Attempt at a Solution I used the dirichlet's function as the template f_n(x)...

How? I can see that x->infinity, e^xf(x)/e^x is of the infinity . limx->inf f(x)/infinity. Since we don't know anything about f(x) except it s continuous and differentiable on (0,infnty), can i make the conclusion that it is not= 0 hence is of the infnty/infnty form. Proceeding with that...

Homework Statement Given f is differentiable on (0,\infty) Given lim_{x->\infty} [f(x)+f'(x)]=L S.T lim f(x)=L and lim f'(x)=0 Hint f(x)=e^{x}f(x)/e^{x} Homework Equations The Attempt at a Solution A Lim _{x->\infty} [f(x)+f'(x)]=L Then for some \epsilon>0...

Homework Statement S.T <f> is not normal. where f is a reflection Homework Equations <f>={e,r^0 f, r^1f,r^2f,..} WTS For any g in D-n, g(r^kf)g^-1 Not In <F> The Attempt at a Solution Elements of D-n are r^k, r^kf For r^k, (r^k)(r^if)(r^-k) is in <f>. So I am stuck

Ok. F'(x)=d/dx(integ f(t)) over 0 to x^2. = f(x).2x=(1/1+x^6).2x

The derivative of an integral is the function itself if it is continuous over the specified region. In this case, the function is not continuous at t=-1, But that is not in 0 to x^2. I don't know how Leibniz rule works here

I got the problem wrong. F(x)=Integ (1+t^3)^-1 from 0 to x^2. Find F'(x) How do I proceed

I tried partial fractions but I landed up with A/(1+t) + B/(1-t+t^2). Cannot find values for A & B that work.

Homework Statement F(X)=[tex]\int[/\frac{1}{1+t^3} Homework Equations The Attempt at a Solution I have tried different substitutions to find fog where g(t) = ? But am getting stuck

I mean pv=0 for a particular v

Homework Statement Let us say that p(c) is a monic polynomial such that when applied to a particular v, we have pv=0. Let V be a finite dimensional vector space. Let V be the direct sum of k invariant subspaces. Then v = v_1+...+v_k. When I apply pv=0 does this imply that pv_1=pv_2=0...

Thank you. You seem to have a way of making it happen!