Need Help Solving Problems in Mathematica

[TitoSmooth]

How do I graph f(x)=x^5-x & g(x)=2 on the same x-y system and zoom into find the crossing points of these 2 functions?

how do I find the terminal velocity(t->infinity) and find 98% of its terminal velocity?

1st step. take the derivative v=24.61(1-(0.27300^t)

then I graph it. but how to find the terminal velocity(t-> infinity) and 98% of it?

How do I check if f(x)=Sqrt of 2+tan^2x.

If it is continuous or not, then find x values corresponding to discontinuities?

This is using Mathematica btw. Thanks

also. is there a help guide that can help me search for commands or a tutorial in layman terms? Mathematica is killing me because I am not computer savvy.

Thanks

 

[TitoSmooth]

Plot[{f[x] == x^(5) - x, g[x] == 2}, {x, -100, 100}] i got this for the first question but my graph is blank.

 

[kduna]

You don't need to write f[x] and g[x] in the plot.


Plot[{x^(5) - x, 2}, {x, -100, 100}] will work.

 

[Bill Simpson]

f[x_] := x^5 - x;
g[x_] := 2;
Plot[{f[x], g[x]}, {x, -100, 100}]

then

Plot[{f[x], g[x]}, {x, -2, 2}]

etc.

Remember that Mathematica is FANATIC about correct capitalization and use of {} versus [] versus () and = versus := versus == and there is even an === and all those are completely different. Make ANY tiny mistake in anyone of those and you will get incorrect results or error messages you don't know what to do with or even nothing at all.

For your terminal velocity question, are you allowed to use the Limit function in Mathematica? If so then look that up in the help system. If not then perhaps repeatedly graphing things over different ranges and trying to estimate the value seems like the only use of Mathematica i can imagine at the moment.

For help you can Google

Mathematica tutorial

or

Mathematica square root

or similar things like that and see if the top few results give you the hint you need.