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) =
The movie Star Wars<span> is a space
opera interstellar epic which uses science and technology in its settings and storylines, although its main
focus is not necessarily on science.</span>
Many
elements in the films appear to defy simple laws of physics.<span>
One of which is the falling of spaceships when they are hit by a laser beam.
Experts said, this is one good example because without gravity in space, ships
should travel in the direction of the impact instead of dropping like a stone.</span>
<span>
</span>
To find the relative distance from one point to another it is necessary to apply the Relativity equations.
Under the concept of relativity the distance measured from a spatial object is given by the equation
Where
= Relative length
v = Velocity of the spaceship
c = Speed of light
Replacing with our values we have that
Therefore the distance between Mars and Venus measured by the Martin is 
