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what is the bit rate 3 30 points consider the characteristics of the f

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Linear Algebra

What is the bit rate?

3. (30 points) Consider the characteristics of the following digitalcommunication system.

a. (8 points) A signal x(t) is used to transmit bits. Shown below is theFourier Transform, X(f) of the signal shown on a frequency scale.

b. (4 points) What percentage of the energy is included from the originalcomplete spectrum?

d. (10 points) Now consider a different signal. What is the maximum bit rate Than can be transmitted over a channel with 100 kHz maximum frequency? 95% of the signal energy is transmitted.

c. (8 points) Show the plot of the time domain signal y(t) that wouldtransmit at twice the bit rate as x(t).

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Question 45665

Linear Algebra

\text { 4] Find } g(0)-g(9)+g(2) \text {, if }
g(x)=\left\{\begin{aligned} \frac{x+1}{2}, & \text { if } x \text { is odd } \\ \frac{x}{2}, & \text { if } x \text { is even } \end{aligned}\right.

Linear Algebra

\text { 3] Find } f(4)-f(2)+f(3) \text {, if }
f(x)=\left\{\begin{array}{ll} \frac{x+1}{2}, & \text { if } x \text { is odd } \\ \frac{x}{4}, & \text { if } x \text { is even } \end{array}\right.

Linear Algebra

2] Find the Domains of the following functions:
\text { a) } f(x)=\sqrt{15-5 x}
f(x)=\frac{x^{2}-2 x+1}{x^{2}-4 x-21}
f(x)=\frac{x^{2}-2 x+1}{\sqrt{16-2 x}}

Linear Algebra

a) Give the definition of a rational function. [5 pts]
b) Give an example of a polynomial function of degree 3. [5 pts]
c) Can a constant function be a polynomial and a rational function at the same time? Explain your answer. [5 pts]
d) Give an example of a non-polynomial function and explain why not apolynomial function. [10 pts)

Linear Algebra

5) Ве,
\begin{array}{c} f: \mathbb{R} \rightarrow \mathbb{R} \\ f(x)=\left\{\begin{array}{ll} x^{2}-3 \cos (\pi x) & x<0 \\ x-4 e^{-2 x} & x \geq 0 . \end{array}\right. \end{array}
Calculate
\int_{-1}^{2} f(x) d x
Presenting the result in simplified form

Linear Algebra

4) Be f: R - Ra function differentiable in R such your derivative f', has in maximum a real zero.
Prove that the equation f(x)=0 has in maximum 2 real square

Linear Algebra

3) Take in consideration the following function
f(x)=\left\{\begin{array}{ll} f: \mathbb{R} \rightarrow \mathbb{R} & \\ \frac{x^{2}-4 x+\cos (\sin (x)),}{x^{4}+4 x^{2}+1}, & x \leq 0 \end{array}\right.
a) Show that the function f is continuous in R+ and in R- but discontinuous in the point X
b) Say justifying, if f is differenciable in X=0

Linear Algebra

2) Prove by definition that
\lim _{x \rightarrow 0} x^{2} \cos \left(e^{x}\right)=0

Linear Algebra

1) Calculate the following limit:
\lim _{x \rightarrow+\infty} \frac{x^{2}\left(e^{-3 x}+1\right)+x \cos (5 x)}{x^{2}+7 x+1}

Linear Algebra

7. Consider the following problem.
Maximize Z = 6X1 + 8X2
5X1 + 2X2 <=20
X1 + 2X2 <=10
X1, X2 >= 0
a. Construct the dual problem for this primal problem
b. Solve both the primal problem and the dual problem graphically.Identify the CPF (Corner-Point Feasible) solutions and corner -pointinfeasible solutions for both problems. Calculate the objectivefunction values for all these solutions.
c. Construct a table listing the complementary basic solutions for theseproblems.
d. Work through the simplex method step by step to solve the primal problem. After each iteration, identify the basic feasible (BF) solution for this problem and the complementary basic solution for the dual problem. Also identify the corresponding corner-point solutions.