Use the following argument to show that

a. Make a sketch of the function f(x) = 1/x on the interval [1, 2]. Explain why the area of the region bounded by y = f(x) and the x-axis on [1, 2] is ln 2.

b. Construct a rectangle over the interval [1, 2] with height 1/2. Explain why ln 2 > 1/2.

c. Show that ln 2" > n/2 and ln 2^-n < -n/    2.

d. Conclude that

Transcribed Image Text:

lim In x = ∞ and lim In x = -∞ 00 x→0+ lim In x = ∞ and lim In x = -∞. x→0* 00 00.