You need to find at least one point in the codomain for which there is no mapping from the domain through f.
In other words, that function can only be surjective if we can choose some x to make f(x) equal to any value we like in R.
Clearly this function is bounded below by its minimum at x...
Howdy Ho, partner.
I have a series of functions {f_{n}} with f_{n}(x) := x^{n} / (1 + x^{n}) and I am investigating the pointwise limit of the sequence f_{n} over [0, 1] to see if it converges uniformly.
I found the pointwise limit f(x) to be f(x) = lim_{n\rightarrow\infty} x^{n} / (1 +...
To find the repeated integral of f over the surface S with respect to dA, where dA is the limit of the small areas on S, I used the fact that dA = R^2 sin\theta \,d\phi \,d\theta.
From there I calculated:
\int \int_{S} f dA = \int^{\pi}_{0} \int^{2\pi}_{0} (3cos\theta 5^2 sin\theta) \...
I have a function f(r, \phi, \vartheta) = 3cos\vartheta.
Evaluating the repeated integral of this function over the surface of a sphere, centered at the origin, with radius 5, I have come up with 0 as my result. I'm not sure if this is correct. I've double checked my calculations, and tried...