Simple equation solving (I think)

[tachu101]

Homework Statement

Find x-intercepts of f(x)= ln(x+1)-(sinx)^2

I know to get to ln(x+1)=(sinx)^2 but have no idea what to do after that.

 

[NoMoreExams]

I don't think it's THAT easy, x = 0 comes to mind though

 

[gabbagabbahey]

It turns out that there are 3 x-intercepts (x=0 is the obvious one). You can estimate what domain they lie in by looking at the maximum and minimum values of $\sin^2(x)$...what are those? What does that tell you about the max/min of $\ln(1+x)$ for which there might be any x-intercepts? You can use that to determine a range of x-values for which x-intercepts are possible.

The next step would be to graph $f(x)$ over that Domain and estimate value for the x-intercepts.

If you are familiar with Newton's method, you can improve your estimations through a few iterative calculations.

 

[NoMoreExams]

This seems to be kind of an overkill for someone in pre-calc though unless you were allowed to use a CAS.

 

[Jamil (2nd)]

Use iteration?

 

[NoMoreExams]

Yes you could use Newton's as was mentioned but I still maintain it's a somewhat hard problem for pre-calc then again I never took pre-calc and maintain that it's a useless class :)