Question

Suponemos que la funcion f(x) = $A + Be^{-x}$ satisface f(0)=4 y f(1)=5-(1/e). Halla el valor de A y de B.

Answer 1

A+Be^(-x)

f(0)=A+Be^(-0)
4= A+B
B= 4-A

f(1)= A + Be^(-1)
5 - (1/e) = A +B/e
(5e-1)/e = (Ae + B)/e
5e-1 = Ae + (4 - A)
5e - 5 = Ae - A
5(e-1)=A(e-1)
A = 5

B=4 - A
B=-1

f(x)= 5 + (-1)e^(-x)