# How can I solve for the intersection points of #y=(x^2)(e^-x)# and #y=1-2sinx# over #2<=x<=7# ?

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I know that there should be 2 intersections within this domain, but which would otherwise be cyclic over #RR# (from what I saw graphically).

I know that there should be 2 intersections within this domain, but which would otherwise be cyclic over

##### 2 Answers

I know of no way to solve this, using algebraic methods. I recommend the use of WolframAlpha

#### Explanation:

Given:

If we attempt to find x coordinates of the points of intersection by asserting

I know of no way to solve this, using algebraic methods. One can use numerical analysis methods such as Newton's Method to find the approximate x values and, then use one of the equations, to obtain the corresponding values of y.

But it is easier to return to the two equations and the domain restriction and give them to WolframAlpha , because the computation engine will give you x and y at the same time.

and

See below.

#### Explanation:

Calling

The iterative process to determine the solutions to

is inspired in the linear approximation using the Taylor expansion of

Now if

Now beginning with a guess near

or

So we found two roots