Proof of Continuous compounding formula - Mathematics Stack …
Following is the formula to calculate continuous compounding A = P e^(RT) Continuous Compound Interest Formula where, P = principal amount (initial investment) r = annual interest …
What is a continuous extension? - Mathematics Stack Exchange
The continuous extension of f(x) f (x) at x = c x = c makes the function continuous at that point. Can you elaborate some more? I wasn't able to find very much on "continuous extension" …
Continuous functions in Sobolev spaces - Mathematics Stack …
Apr 16, 2023 · Here instead of starting with the Lp L p space and selecting continuous elements, we had to complete the space of continuous functions on the boundary formed by the …
is bounded linear operator necessarily continuous?
In general, is a bounded linear operator necessarily continuous (I guess the answer is no, but what would be a counter example?) Are things in Banach spaces always continuous?
Proof that the continuous image of a compact set is compact
I know that the image of a continuous function is bounded, but I'm having trouble when it comes to prove this for vectorial functions. If somebody could help me with a step-to-step proof, that …
probability theory - Why does a C.D.F need to be right-continuous ...
May 10, 2019 · This function is always right-continuous. That is, for each x ∈ Rk x ∈ R k we have lima↓xFX(a) =FX(x) lim a ↓ x F X (a) = F X (x). My question is: Why is this property important? …
Prove that $\\sqrt{x}$ is continuous on its domain $[0, \\infty).$
As you have it written now, you still have to show x−−√ x is continuous on [0, a) [0, a), but you are on the right track. As @user40615 alludes to above, showing the function is continuous at …
general topology - Proving injective continuous function is ...
Jun 24, 2019 · Proving injective continuous function is homeomorphism [duplicate] Ask Question Asked 6 years, 6 months ago Modified 6 years, 6 months ago
The definition of continuously differentiable functions
Jan 24, 2015 · Note the ending "-ly", which makes it an adverb, not an adjective. So "continuously differentiable" means "differentiable in a continuous way".
measure theory - Are right continuous functions measurable ...
15 Are right-continuous function from Rn R n to R R necessarily semi-continuous? If not, are they necessarily Borel measurable? Is there a topological characterization of right-continuous …