y = {x-[(x^2)+1]^(1/2)} / {x+[(x^2)+1]^(1/2)}
(2) Find the following limits,
(a) lim(x→0) [ln(1+x)] / (x)
(b) lim(x→∞) [ln x] / [x^(1/6)]
(c) lim(x→∞) [x^(2)] / [e^(x)]
(3) Evaluate the following integrals
(a) ∫ (1) / [(x^2)(1+x^2)^(1/2)] dx
(b) ∫ [2sec(1/x)] / [x^(2)] dx
(c) ∫ [(ln x)^(2)] / (x) dx
(d) ∫ [x^(3)] / [1+x^(2)] dx
(e) ∫ x[e^(2x)] dx
(4) Evaluate the areas of the region R bounded by the x-axis and the curve
y = 1 + sin x between x = 0 and x = 3π/2
更新1:
(3b) is ∫ [2sec(1/x)] / [x^(2)] dx
更新2:
Is [ -∫ sec y dy ] not equal to [ -ln (sec y + tan y ) + C ] ?
