Question

1. Consider the equation 2 x e x + = . This equation has a solution close to x = 0 .

a. Determine the linear approximation, L x( ), of the left-hand side of the equation about
x = 0 . (2)
b. Use L x( ) to approximate the solution of the equation 2 x e x + = . (2)

Answer 1

the linear approximation formula is based on the equation of the tangent line of a function at a fixed point. The linear approximation of a function f(x) at a fixed value x = a is given by L(x) = f(a) + f '(a) (x - a).

Explanation: