limx→∞ arccos{(1+x²)/(1+2x²)} find limit.∫√3/4, 0 dx/1+16x²；∫π/2, 0 sinx/1+cos²x * dx；∫1/x√x²-4 * dx；evaluate the integral.
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(1) The limit is π/3
(2) The indefinite integral is (1/4) tan^-1(4x) + C
Applying the limits, the answer is π/12
(3) The indefinite integral is -tan^-1(cos x) + C
Applying the limits, the answer is π/4
(4) The answer is (1/2) tan^-1 {2/√(x^2 - 4)} + C
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