Consider the space P2 with inner producti r' (f.g) = j J ( f(t)g(t)dt.Find an orthonormal basis of the space of all functions in P2 that are orthogonal to / (r) = t.

L22 - 5 Diﬀerentials Def. Let y = f(x)b eaieaelni. The diﬀerential dx is an independent variable (it can be any real number). The diﬀerential dy or d(f(x)) is a dependent variable deﬁned by x ex. 1) Find dy if y = f(x)= 2. 3 − x 2) Evaluate dy when x =2a nd dx = −0.02.