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

Click For 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
Messages
1,447
Reaction score
5
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!
 
Physics news on Phys.org
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.
 

Thread 'Magnitude of buoyant force in fluids of different densities'

The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?
View full post »

Similar threads

Solve Numerical Problems: 4x^2 - e^x = 0
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad The algorithms involved in finding a solution with numerical methods
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Numerically solving Time-independent Schrödinger eqn. using Shooting algorithm
  • · Replies 20 ·
Replies
20
Views
3K
Numerically find temperature in function of concentration....
  • · Replies 4 ·
Replies
4
Views
2K
How does one convert a decimal float to binary using the multiply by 2 method?
  • · Replies 4 ·
Replies
4
Views
2K
Graduate How do I apply the method of steepest descents to this integral?
  • · Replies 1 ·
Replies
1
Views
2K
How should I show that this root is given approximately by this?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How Do Roster and Set Builder Methods Enhance Traditional Topics?
  • · Replies 6 ·
Replies
6
Views
2K
Solve ##\int\frac{e^{-x}}{x^2}dx## and ##\int \frac{e^{-x}}{x}dx##
  • · Replies 7 ·
Replies
7
Views
2K
MHB Solving Equations Using Bisection, Newton, and Secant Methods
  • · Replies 8 ·
Replies
8
Views
3K