Homework Statement
Suppose f is integrable for all x in[a,b] and f(x)>C ( C is some constant),
Must show that 1/f is also integrable.
Homework Equations
f is integrable implies Upf-Lpf<\epsilon for some partition in [a,b]
The Attempt at a Solution
Therefore, I must come up...
I'm new in java and
I'm trying to come up with a program that stimulates the bean machine(also known as Galton box)
Balls are dropped from the opening of the board. Everytime a ball hits, there is a 50% chance to fall to left and 50% chance to fall to the right. the piles of balls are...
the inequality makes sense now that you explained,
I still have trouble proving it,
Where do I use the fact that f is TWICE differentiable?Does that make a difference?
r twice continuously differentiable function proof...
Homework Statement
Help :frown:
if f:[a,b] \rightarrow R is twice continuously differentiable, and f(x)\geq 0 for all x in [a.b]
and f ''(x) \leq 0 for all x in [a,b]
prove that
1/2 (f(a) + f(b)) (b-a) \leq \int f(x)dx \leq(b-a)...
right,
But I think you made a little mistake with differentiation,
I think it will be:
F'(x)= 2x sin(1/x2) - 2cos(1/x2)/ x
Which still, limits exists.
But How do I prove that F'(x) is unbounded?
hey guys,
Any one can think of any examples ?
Of a sequence of integrable functions{fn} on [0,1] that converges pointwise to a non-integrable function f:[0,1] --> R
??
Homework Statement
Consider
F(x) = x2 sin(1/x2) if 0<x\leq1
and = 0 if x\leq0
Show that F'(x) exists for all x \in[a,b] but that F':[0,1] \rightarrow1 is not integrable.
Homework Equations
So we have to show we do not have F(1)-F(0) = \int F'(x)dx
(integral...
Homework Statement
f:[0,1] \rightarrow R is a continuous function such that
\intf(t)dt (from 0 to x) = \int f(t)dt( from x to 1) for all x\in[0,1] .
Describe f.
Homework Equations
integral represents area
The Attempt at a Solution
what ever the function is, I know that...
Hey guys,
Can you help me prove this?
Suppose that f:[a.b] -> R is integrable and that F:[a,b]->R is a differentiable function such thet F'(x)= f(x) for all xLaTeX Code: \\in [a,b].
Prove from the definition of the integral that;
F(b)-F(a) =LaTeX Code: \\int f(x) dx ( integral going from...
Hey guys,:smile:
Can you help me prove this?:confused:
Suppose that f:[a.b] -> R is integrable and that F:[a,b]->R is a differentiable function such thet F'(x)= f(x) for all x\in [a,b].
Prove from the definition of the integral that;
F(b)-F(a) =\int f(x) dx ( integral going from a to b)...