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- The Wronskian1. Show that the functions ex, cos x and sin x are linearly independent.2. Show that 1, sin2 x and cos2 x are linearly dependent.Prove using the IVT cosx = cos-1x has a solution in (0, 1).Differentiate the following with respect to x using appropriate rule 1) (2-5x)^ 3/2 2) 2x^3 cos 3x 3) 2x+1 / 3x-4
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- Suppose that|x + 4| < 0.024 and |y − 6|< 0.04. Use the triangle inequality to show that |(x + y) − 2|< 0.024 Express 1\2 ln x + 5 ln y − 2 ln z as a single term Simplify the following: sin 3x\sin x −cos 3x\cos xIn the integration of (cos x)^4 (sin x)^3 dx, what is the appropriate transformation? Transform (cos x)^2 to 1/2(1 + cos 2x) Transform (sin x)^2 to 1 - (cos x)^2 All options are incorrect Transform (cos x)^2 to 1 - (sin x)^2Given (cos3x)^2 = 0.5(cos6x+1). The above identity is actually the Fourier series of (cos3x)^2x true or false?