a Suppose that (x) is differentiable for all x in 0, 1 and that (0) 0 Define sequence a n by the rule a n n(1 n) Show that lim n an (0) Use the result in part (a) to find the limits of the following sequences a n b c d an n tan n

Question: a. Suppose that (x) is differentiable for all x in [0, 1] and that (0) = 0. Define sequence {a n } by the rule

a. Suppose that ƒ(x) is differentiable for all x in [0, 1] and that ƒ(0) = 0. Define sequence {a_n} by the rule a_n = nƒ(1/n). Show that lim_n→∞an = ƒ′(0). Use the result in part (a) to find the limits of the following sequences {a_n}.

b. = an n tan n

= an n tan n

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