-- It takes the brick 8.9 seconds to reach the ground.
-- At the instant of the "splat", it's falling at 89 m/s.
-- The mass doesn't matter. If not for air resistance, every object
would fall at the same rate. The answer is the same for a feather,
a rubber chicken, a brick, or a school bus.
<span>The salad dressing is known as a compound dressing. A compound is simply a combination, or mixture, of two or more ingrediants.
Physical properties include, density, hardness, melting, and boiling points. Flammability is considered a chemical property along with vapor, concentration, etc.
Wood is not a reliable conductor for heat, while Copper is considered the best.</span>
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) =
