Re: inequations & trig. eq
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Re: inequations & trig. eq
Hi, Thanks a lot for the answer
Yes, but how to solve x/(x-1) undefined ?
and if the inequation is a little bit difficulter for ex
(sinx-2)/(4sin^2 x -1)>2
Many thanks in advance
Sincerely
Ser
>
> Yes the TI-85/86 can be used for solving Trig. equations and
> solving inequalites.
>
> Use graphing and use SOLVER to find solutions to equations, these
> same procedures that work for equations in general will work for
> the specific trig. equations.
>
> Graphing, SOLVER, and POLY, can also aid in solving inequalities.
>
> Theorem: Let f(x) be any expression with the single variable x.
> Then for any real number a one of the following must be true:
>
> 1. f(a)=0
>
> 2. f(a)>0
>
> 3. f(a)<0
>
> 4. f(a) is undefined.
>
> To solve f(x)>0 or f(x)<0 first solve f(x)=0 and f(x) undefined.
>
> Example:Solve x/(x-1) > 0
>
> Solution: Fisrt solve x/(x-1)=0 and x/(x-1) undefined.
>
> x=0 x = 1
>
> Plot these 'critical' points.
>
> <-----------------0-----------1---------------->
>
> Note the real number line is cut into three regions. Use a test
> point for each region. A test point should be completely inside
> the region. -10 will work for the left region, .5 for the middle
> region , and 20 for the right region. (Any point in a region will do.)
> Check each of these test points. If the test point checks so
> does all the other points in same region it comes from. If it does not
> then none of the other of that region will check either.
>
> <-----------------0-----------1---------------->
> -10 .5 20
>
> -10/(-10-1) > 0 .5/(.5-1) > 0 20/(20-1) > 0
>
> Yes No Yes
>
> So the solution to
>
> x/(x-1) > 0
>
> is
> x<0 or x>1
>
> To find these 'critical' values and to check the test points
> calculators can be of great assistance. The TI-85/86 is truely
> great at this.
>
> The graphing features of TI-85/86 can also be used in solving
> inequalites.
>
> If you graph y=x/(x-1)
>
> 1. The x-intercepts correspond to where x/(x-1)= 0.
>
> 2. The region(s) where the graph is above the x-axis corresponds to the
> subset where x/(x-1)>0.
>
> 3.The region(s) where the graph is below the x-axis corresponds to the
> subset where x/(x-1)<0.
>
> 4.The region(s) where there is no graph corresponds to where x/(x-1)
> is undefined.
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