The statement about pointwise convergence follows because C is a complete metric space. If fn → f uniformly on S, then |fn(z) − fm(z)| ≤ |fn(z) − f(z)| + |f(z) − fm(z)|, hence {fn} is uniformly Cauchy. Conversely, if {fn} is uniformly Cauchy, it is pointwise Cauchy and therefore converges pointwise to a limit function f. If |fn(z)−fm(z)| ≤ ε for all n,m ≥ N and all z ∈ S, let m → ∞ to show that |fn(z)−f(z)|≤εforn≥N andallz∈S. Thusfn →f uniformlyonS.
2. This is immediate from (2.2.7).
3. We have f′(x) = (2/x3)e−1/x2 for x ̸= 0, and f′(0) = limh→0(1/h)e−1/h2 = 0. Since f(n)(x) is of the form pn(1/x)e−1/x2 for x ̸= 0, where pn is a polynomial, an induction argument shows that f(n)(0) = 0 for all n. If g is analytic on D(0,r) and g = f on (−r,r), then by (2.2.16), g(z) =
I think you forgot to give the options along with your question. I am answering the question based on my knowledge and research. <span>A business that sells products to teens would most likely create a website with a title ending in .com. I hope that this is the answer that has actually come to your great help.</span>
The answer is energy.
Waves in the ocean are energy travelling along water.
Waves do not transport mass, they transport energy, this is the ability to perform work or exert force and distant points.
Although water seems to be travelling along with the wave, the molecules of water only move up and down; they do not travel along with the wave.
The higher the pressure, the higher boiling point of water. At lower the pressure, the boiling point of water comes down. So, the lower pressure inreases the boiling resulting more evaporation. As we go higher in altitude, the atmospheric pressure decreases. This results in decreasing the boiling point at higher altitude and increase in boiling of water. In fact, at the sea level ,the the sea water boils at 100 degree C where atmospheric pressre is normal. However , the boiling takes place at a lower temperature at the top of a mountain due to low pressure. In other words the boling is faster at the top of a mountain than that at its foot.
Answer:
B on edge
Explanation:
the piles of the magnetic field generated around the armature are attracted to the opposite poles of the permanent magnent. As the opposite poles align, the commutator reverses the current direction so like poles are aligned and the armature continues to spin
