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.

Solutions

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 1 year ago

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