大学微积分问题着急（哪位大神详细求解！！！）
1.Simplifytheexpressionsin（2cos^-16x）.2.Letf(x)=sin^-1x.FindalinearapproximationofFat...
1. Simplify the expression sin（2cos^-1 6x）.
2. Let f(x) = sin^-1 x. Find a linear approximation of F at x = a = 1/2 and use this linear approximation to predict the value of the function at x=3/4 展开
2. Let f(x) = sin^-1 x. Find a linear approximation of F at x = a = 1/2 and use this linear approximation to predict the value of the function at x=3/4 展开
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1)
令 cos^-1 6x = A
==> cosA = 6x/1, and sinA = +/-√(1-36x^2)
sin（2cos^-1 6x）= sin2A = 2sinAcosA = +/-12x√(1-36x^2)
2）
f'(x) = 1/√(1-x^2) = 2/√3 at x = 1/2
f(3/4) ~ f(1/2) + f'(1/2)(3/4-1/2) = π/6 + (2/√3)(1/4) = .8123
令 cos^-1 6x = A
==> cosA = 6x/1, and sinA = +/-√(1-36x^2)
sin（2cos^-1 6x）= sin2A = 2sinAcosA = +/-12x√(1-36x^2)
2）
f'(x) = 1/√(1-x^2) = 2/√3 at x = 1/2
f(3/4) ~ f(1/2) + f'(1/2)(3/4-1/2) = π/6 + (2/√3)(1/4) = .8123
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