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) f(x) = x^4 - 1/- 1 The discontinuity is removable The discontinuity Is not removable g(x) = f(x) = x^3 - x^2 - 20x/x - 5 The discontinuity is removable The discontinuity Is not removable 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) = DNE

Explanation / Answer

a)discontinuity is removable

g(x)=(x4-1)/(x-1)

g(x)=((x2)2-12)/(x-1)

a2-b2=(a+b)(a-b)

g(x)=(x2+1)(x2-1)/(x-1)

g(x)=(x2+1)(x+1)(x-1)/(x-1)

g(x)=(x2+1)(x+1)

b)discontinuity is removable

g(x)=(x3-x2-20x)/(x-5)

g(x)=x(x2-x-20)/(x-5)

g(x)=x(x2-5x+4x-20)/(x-5)

g(x)=x(x(x-5)+4(x-5))/(x-5)

g(x)=x(x-5)(x+4)/(x-5)

g(x)=x(x+4)

c)discontinuity is not removable

g(x)=DNE

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