Evaluate the function f(x) at the given numbers (correct to six decimal places).

Question

Evaluate the function f(x) at the given numbers (correct to six decimal places). f(x) = x2 - 6x / x2 - x - 30, x = 6.5, 6.1, 6.05, 6.01, 6.005, 6.001, 5.9, 5.95, 5.99, 5.995, 5.999 f(6.5) = f(6.1) = f(6.05) = f(6.01) = f(6.005) = f(6.001) = f(5.9) = f(5.95) = f(5.99) = f(5.995) = f(5.999) = Guess the value of the limit of f(x) as x approaches 6, correct to six decimal places. (If an answer does not exist, enter DNE.) limx rightarrow 6 x2 - 6x / x2 - x - 30 =

Explanation / Answer

f(x) = [x^2 - 6x]/[x^2 - x - 30] f(6.5) = 0.565217 f(6.1) = 0.549549 f(6.05) = 0.547511 f(6.01) = 0.545867 f(6.005) = 0.545661 f(6.001) = 0.545496 f(5.9) = 0.541284 f(5.95) = 0.543378 f(5.99) = 0.545041 f(5.995) = 0.545248 f(5.999) = 0.545413 limx-->6 [x^2 - 6x]/[x^2 - x - 30] apply L'Hospital's rule = lim x-->6 [2x - 6]/[2x - 1] = 12-6 /12-1 = 6/11 =0.545454

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