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**coley0412** Hi, I'm hoping someone can help me get started with this problem as I'm not entirely sure what they're looking for:

We wish to approximate the function $\displaystyle x(t) = e^{t}$

over the interval (0, 1), using a second order polynomial.

a). From the set of linearly independent function,$\displaystyle [1, t, t^{2}]$form an orthonormal set of functions. The inner product is defined as $\displaystyle <f(t), g(t)>=\int_0^1\! f(t)g(t) \, \mathrm{d}x$

b). Based on this set of orthonormal functions, fit the best approximation in the least square error sense, that is minimize the norm of the error between the function x(t) and its approximation.

I think I understand how to approximate the function but I'm not sure how to get an orthonormal set of functions or part b. Any help would be appreciated - thanks!!