Find the linear approximation at x = 0 to show that the following commonly used approximations are valid for "small" x. Compare the approximate and exact values for x = 0.01, x = 0.1, and x = 1. Round your calculations to seven decimal places if needed. 3tan(x) ? 3x L(x) f(x) x = 0.01 x = 0.1 x = 1 Note: f(x) = 3tan(x)
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The linear approximation of a function at a point a is given by the formula L(x) = f(a) + f'(a)(x - a). The derivative of f(x) = 3tan(x) is f'(x) = 3sec^2(x). At x = 0, f(0) = 3tan(0) = 0 and f'(0) = 3sec^2(0) = 3. So, the linear approximation at x = 0 is Show more…
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