Plot π(x), Li(x),x/ln(x) in Mathematica for each of the following ranges: 2≤x≤10,000; 10,000≤x≤20,000; and,100,000≤x≤110,000.

Expert Solution

For the mathematica command is PrimePi [x].

For Li(x) the mathematica command is LogIntegral [x].

For x/ln(x) the mathematica command is x/Log[x].

So to plot these in the range , the command becomes :

Plot [ {PrimePi[x], LogIntegral [x], x/Log[x] }, {x,2,10000}, PlotStyle -> {Red, Blue, Green}, Axes->True]

Similarly, to plot these in the range , the command becomes :

Plot [ {PrimePi[x], LogIntegral [x], x/Log[x] }, {x,10000, 20000}, PlotStyle -> {Red, Blue, Green}, Axes->True]

And, to plot these in the range , the command becomes :

Plot [ {PrimePi[x], LogIntegral [x], x/Log[x] }, {x,100000, 110000}, PlotStyle -> {Red, Blue, Green}, Axes->True]

[In all the above cases, the first graph (that is pi(x)) will appear in red, the graph for li(x) in blue and the third one will appear in green.]

Let me know anything is not clear!

Colby Messinger answered 2 years ago

Give the domains and ranges of the following functions. A) ln x, B) cos X, C)...

Give the domains and ranges of the following functions. A) ln x, B) cos X, C) 10^x D) f(x)= 1/ x^2-12x-45 E) g(x)= sqrt(82-x).

f(x,y)=sin(2x)sin(y) intervals for x and y: -π/2 ≤ x ≤ π/2 and -π ≤ y ≤...

f(x,y)=sin(2x)sin(y) intervals for x and y: -π/2 ≤ x ≤ π/2 and -π ≤ y ≤ π find extrema and saddle points In the solution, I mainly interested how to findcritical points in case of the system of trigonometric equations (fx=0 and fy=0). ,

2. Evaluate the following limits. (a) lim x→1+ ln(x) /ln(x − 1) (b) limx→2π x sin(x)...

2. Evaluate the following limits. (a) lim x→1+ ln(x) /ln(x − 1) (b) limx→2π x sin(x) + x ^2 − 4π^2/x − 2π (c) limx→0 sin^2 (3x)/x^2

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 +...

Using the definition of an anti-derivative, prove that x (ln x)3 – 3x (ln x)2 + 6x (ln x) – 6x is an anti-derivative of (ln x)3 (must show all work)

Write as a MatLab script For X=-2π~2π with intervals of π/100. a. Plot Y1=sin(X) as a...

Write as a MatLab script For X=-2π~2π with intervals of π/100. a. Plot Y1=sin(X) as a red line. Add a grid. b. Plot Y2=cos(X) as a black dotted line. Add a grid. c. Plot Y1 and Y2 in the same plot without using the hold on/off command. d. For Y3= Y1 times Y2, plot Y1, Y2 and Y3 in the same graph. Y3 will be green line. Add title, axis label and a legend.

Donald Gilmore has $100,000 invested in a 2-stock portfolio. $20,000 is invested in Stock X and...

Donald Gilmore has $100,000 invested in a 2-stock portfolio. $20,000 is invested in Stock X and the remainder is invested in Stock Y. X's beta is 1.50 and Y's beta is 0.70. What is the portfolio's beta? Zacher Co.'s stock has a beta of 1.12, the risk-free rate is 4.25%, and the market risk premium is 5.50%. What is the firm's required rate of return? Porter Plumbing's stock had a required return of 14.25% last year, when the risk-free rate...

If a business has $100,000 in net income, $20,000 in advertising expenses, $10,000 in accounting fees,...

If a business has $100,000 in net income, $20,000 in advertising expenses, $10,000 in accounting fees, and a $40,000 positive effect in foreign currency adjustments, then what is their comprehensive income?

Using matlab Find x and y that solve the following system: ln(x 2 + y) =...

Using matlab Find x and y that solve the following system: ln(x 2 + y) = 1 − y , xy = − √ x

Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1. Determine and plot the spectrum Fourier Transform of...

Consider the following periodic signal : x(t)=∑∞n=−∞Π(t−4n2). 1. Determine and plot the spectrum Fourier Transform of signal x(t) ( For plot : Use only interval n=-2 to n=2). 2. Based on the result obtained in part one. Determine Complex Exponential Fourier Series, and trigonometric Fourier Series. 3. Evaluate the energy spectral density of the periodic signal x(t) in rang (n=-2 to n=2)

The following reaction was monitored as a function of time: A→B+C A plot of ln[A] versus...

The following reaction was monitored as a function of time: A→B+C A plot of ln[A] versus time yields a straight line with slope −4.0×10−3 /s . Part D If the initial concentration of A is 0.220 M , what is the concentration after 230 s ? [A] = m M

Question