How Do You Solve 4x^2 - e^x = 0 Using Numerical Methods?

AI Thread Summary
To solve the equation 4x^2 - e^x = 0, one approach is to expand e^x using a Taylor series. Another suggestion is to use the bisection method, though the challenge lies in selecting appropriate initial points for this method. Plotting the functions y1(x) = 4x^2 and y2(x) = e^x can visually reveal their intersections, indicating the solutions. The discussion emphasizes the importance of identifying intervals containing solutions for effective numerical methods. Overall, various numerical techniques can be employed to tackle this equation.
stunner5000pt
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Find the intervals containing solutions to the following equation

4x^2 - e^x = 0
I haven o clue on where to start really?
WOuldi expand e^x using taylor series? i mean one could do this
x - 2ln x = ln 4
so then would i do log expansion by taylor series? Or would i use bisection method? But how owuld i pick the two points for bisection method? Please assist!

And as always, your help is greatly appreciated!
 
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stunner5000pt said:
Find the intervals containing solutions to the following equation

4x^2 - e^x = 0
I haven o clue on where to start really?
WOuldi expand e^x using taylor series? i mean one could do this
x - 2ln x = ln 4
so then would i do log expansion by taylor series? Or would i use bisection method? But how owuld i pick the two points for bisection method? Please assist!

And as always, your help is greatly appreciated!

Why not just plot:

y1(x)=4x^2

and

y2(x)=e^x

interesections, bingo-bango.
 
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