Which of the following functions f has a removable discontinuity at a? If the di

Question

Which of the following functions f has a removable discontinuity at a? If the discontinuity is removable, find a function g that agrees with f for x notequalto a and is continuous at a. (If an answer does not exist, enter DNE.) (a) f(x) = x^4 - 1/x - 1, a = 1 The discontinuity is removable. The discontinuity is not removable. g(x) = (x + 1)(x^2 + 1) b) f(x) = x^3 - x^2 - 12x/x - 4, a = 4 The discontinuity is removable. The discontinuity is not removable. g(x) = x(x + 3) (c) f(x) = [[sin(x)]] a = pi (Recall that [[h(x)]] means the largest integer that is less than or equal to h(x).). The discontinuity is removable. The discontinuity is not removable. g(x) = -1

Explanation / Answer

f() has a not removable discontinuity

and since

big bracket means that least value is taken

and at =pi

f(x) =0

so g(x) = 0

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