a. Show that -1/2 x/(1 + x 2 ) 1/2 for every value of x. b. Suppose that is a function whose

a. Show that -1/2 ≤ x/(1 + x²) ≤ 1/2 for every value of x.

b. Suppose that ƒ is a function whose derivative is ƒ′(x) = x/(1 + x²). Use the result in part (a) to show that

for any a and b.

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