Please help with example problems 1-3.

1.

\f2] Let f be continuous on [a, b], differentiable on (a, b) and positive (i.e., > 0) for all a? E (a, b). Prove that there 3:55) = + Fla. (Hint: consider the function F (33) = (33 a) (if 5) ft\") and use MVT for F (3:) to show the existence of such 6 E (a, b).) exists 0 E (a, 5) such that 3) Use L'Hopital's Rule to evaluate and check your answers numerically: sin x (a) lim 1 1 (b) lim sin' x