x+1=e^x the question is solve?
You can't solve this problem exactly. You can do 2 things (1) guess the solution. (2) use numerical approximation. (3) graph x+1 and e^x and find where the 2 curves intersect. It happens that's this equation is simple to solve by guessing.
as an infinite sum: e^x = 1 + x + (1/2!)*x^2 + (1/3!)*x^3 + .... x + 1 = 1 + x + (1/2!)*x^2 + (1/3!)*x^3 + ... 0 = (1/2!)*x^2 + (1/3!)*x^3 + .... x^2 * ( (1/2!) + (1/3!)*x + (1/4!)*x^2 + ...) = 0 Giving x = 0, using Newton Method we get: x(n+1) = x(n) -1 + x(n) / (e^x(n) -1) from which we might be able to form a proof that x =0 is the only solution
As uweddie said, graph them and see where they intersect.
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