Approximating In 2 Consider the following three ways to approximate In 2.

a. Use the Taylor series for In (1 + x) centered al 0 and evaluate it at x = 1(convergence was asserted in Table 9.5) write the resulting infinite series. resulting infinite series.

b. Use the Taylor series for In (1 − x) centered at 0 and the identity In . Write the resulting infinite series.

c. Use the property In (a/b) = In a − In b and the series of parts (a) and (b) to find the Taylor series for centered at 0.

d. At what value of x should the series in part (c) be evaluated to approximate In 2? Write the resulting infinite series for In 2.

e. Using four terms of the series, which of the three series derived in parts (a)-(d) gives the best approximation to In 2? Which series gives the worst approximation? Can you explain why?

Infinite and Negative Words 2/9/17 Indefinite Words Algo – something, anything Alguien – someone, somebody, anyone Alguno/a(s), algun – some, any o…o – either, or siempre – always tambien – also, too Negative Words Nada – nothing, not anything Nadie – no one, nobody, not anybody Ninguno/a(s),...