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- For what x-value (approximately) does the function f (x) = sin(x) − x reach height -2? (Use x = 2 as a first approximation, use at least 5 decimal places in your calculation, and continue until at least 3 decimal places are correct or stable.)How do I find the 20th derivative of f(x)=(2cos x)(cos 3x)? I think there must be some trick because this was on a timed test with about 40 questions.Find and locate the local and absolute extreme values of f(x) = x+(sin2x)in [0, π].
- Consider ∫ x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)?(a) From sin2 x + cos2 x = 1, we have f(x) + g(x) = 1. Take the derivative of both sides of this equation to obtain f' (x) + g' (x) = 0. This implies f'(x) = -g'(x). (b) f' (x) = 2 sin x cos x, and g'(x) = 2(cosx)(-sinx) = -2sin x cos x. So, f'(x) = -g'(x).Compare the accuracies of the approximations sin x = x and sin x = 6x/(6 + x2) by comparing the graphs of ƒ(x) = sin x - x and g(x) = sin x - (6x/(6 + x2)). Describe what you find.