Consider the functions (x) = 1/1 + x 2 and g(x) = 1/1 + x 4 .

Consider the functions ƒ(x) = 1/√1 + x² and g(x) = 1/√1 + x⁴.

(a) Use your calculator to approximate ∫₁^b f(x) for b = 20, 50, 100, 1000, and 10,000.

(b) Based on your answers from part (a), would you guess that  ∫₁^∞ f(x) dx is convergent or divergent?

(c) Use your calculator to approximate ∫₁^b f(x) for b = 20, 50, 100, 1000, and 10,000.
(d) Based on your answers from part (c), would you guess that  ∫₁^∞ f(x) dx is convergent or divergent?

(e) Show how the answer to parts (b) and (d) might be guessed by comparing the integrals with others whose convergence or divergence is known.