Please see the attached file for the fully formatted problems. Let g be a function which can be differentiated four times on the interval [-1,1]. Denote . 1) Show that when g is a polynomial of degree less than or equal to 3. 2) Let P be the interpolation polynomial of f at the points -1, , , 1. a) Show that . b
Let z be a complex number z=x+iy x <>0 and y<>0 Prove: 1. If z+1/z is real then |z|=1 2. If |z|=1 then z+1/z is real
Polynomial with real coefficient
When the accountants for lose-a-digit Computer, Inc. had finished preparing their annual budget, they presented the final figures to the president, I.M. Smart. "It looks like a good year," he exclaimed. "The amount of the budget just happens to be the smallest number of cents (other than one cent) that is a perfect square, a per
Simplify: (a/(a-b))+(b/a^2+ab+b^2))- (2/(a^3-b^3)
(a) Let G = GL(2,R) be the general linear group. Let H=GL(2,Q) and K= SL(2,R) = {A is an element of G: det (A) =1} Show that H,K are subgroups of G (b) Let p be a prime number and a is an element of Z. Prove that a^p ,is equivalent to, a mod p
Prove: There are infinitely many prime numbers p of the form 4n+3. In other words, show that there exist infinitely many positive integers, n, such that the number 4n+1 is prime.
Use a taylor polynomial to show that , for a large wavelength, Planck's Law gives approximately the same values as the Rayleigh-Jeans Law. see the attached problem #2
Prove the following conjectures, that for all N in the set of Natural Numbers... Question continued in attachment.
What is (6^6)+(6^5) in (mod5)?
What is the ones digit of the number (23)^23?
The natural number 28A9B consists of different numbers and A is not equal to 0. When the number is divided by 9 the remainder is 7 and when it is divided by 5, the remainder is 1. What is A-B=?
What is the result of ((-1/2)^-3)^2?
What is the result of 0.1/0.01 + 0.01/0.001 + 0.001/0.0001=?
Show that the square root of a prime number is not rational.