Which business structure is characterized by having unlimited liability for its owners?

• A. Corporation
• B. Limited Liability Company (LLC)
• C. Sole Proprietorship
• D. Partnership
• E. Cooperative
•  

3. Let fn(2) be a sequence of functions defined on [0,1] converging uniformly to a function f(x). Show that if each fn (2) is Riemann integrable on [0,1], then so is f(x) and So fn(x) dx converges to f f(x) dx. 4. If A is a diagonalizable matrix, prove that A is diagonalizable if and only if its minimal polynomial has no repeated roots. 5. State and prove the spectral theorem for compact self-adjoint operators on a Hilbert space. 6. Determine whether there exists a holomorphic function on the unit disk such that f(1/n) = (-1)"/n for all positive integers n. 7. Prove the prime number theorem: Let (2) denote the number of primes less than or equal to z. Show that limo z/In(z) (2) = 1. 8. Let f be an analytic function on a domain D and suppose f'(z) = 0 for all z in D. Prove that f must be a constant function on D. 9. Given a bounded linear operator T on a Hilbert space H, prove that T* is the unique bounded linear operator on H such that (Tx, y) = (x, T*y) for all x, y in H, where T* denotes the adjoint of T. 10. Demonstrate that the category of topological vector spaces and continuous linear maps has all direct sums and all direct products.