Question

Why we can let sequence an=1/2n(pi) to be a sequence of function 2xsin(1/x)-cos(1/x)??? Please explain it.

Answer #1

Is fx(X) = c[1 + cos(x)] a valid probability density function
over the interval -pi <= x <= pi? If so, please show your
reasoning why and solve for c if applicable?

if f''(x)= -cos(x)+sin(x), and f(0)=1 and f(pi)=), what is the
original function

Explain why each sequence diverges:
{cos nπ}
{1+(-1)^n}
{sqrt(n)}

(a) Let E be an encryption function and A a function that can be
used to compute a
message authentication code. Let x be a message. Alice computes
E(A(x)jx) and
sends it to Bob. Is this an example of encrypt-and-MAC,
encrypt-then-MAC or
MAC-then-encrypt?
(b) Let E be an encryption function and A a function that can be
used to compute a
message authentication code. Let x be a message. Alice computes
E(x)jA(x) and
sends it to Bob. Is this an...

let f(x)=cos(x). Use the Taylor polynomial of degree 4
centered at a=0 to approximate f(pi/4)

Prove that f(x)=x*cos(1/x) is continuous at x=0.
please give detailed proof. i guess we can use squeeze
theorem.

Let h be the function defined by H(x)= integral pi/4 to x
(sin^2(t))dt. Which of the following is an equation for the line
tangent to the graph of h at the point where x= pi/4.
The function is given by H(x)= integral 1.1 to x (2+ 2ln( ln(t) ) -
( ln(t) )^2)dt for (1.1 < or = x < or = 7). On what
intervals, if any, is h increasing?
What is a left Riemann sum approximation of integral...

I know that sequence cos(1/n) is bounded but how to show that
the sequence {cos(1/n) is also monotonic
Please write clearly

fourier expansion, piecewise function.
f(x){ pi , -1<x<0
-pi , 0<x<1

Prove that the family of trigonometric functions { 1, cos x, sin
x, ..., cos nx, sin nx, ...} form an orthogonal system on [-pi,pi]
prove that the following orthogonality relations
hold integral from -pi to pi of sin nx dx = 0 and integral from
-pi to pi of cos nx dx = 0

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