a. Suppose that f(x) is differentiable for all x in [0,1] and that f(0)=0 . Define sequence {…

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a. Suppose that f(x) is differentiable for all x in [0,1] and that f(0)=0 . Define sequence {a_n} by the rule a_n=n f(1 / n) . Show that lim_n →∞ a_n=f^'(0) . Use the result in part (a) to find the limits of the following sequences {a_n} . b. a_n amp;=n tan^-1 1/n amp; c. a_n=n(e^1 / n-1)
d. a_n amp;=n ln(1+2/n)

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