Question

8. Find all discontinuities of f(x) = (x4 - 1)/(x2 - 4)(x - 1). Explain in detail which discontinuities, if any, are removable and which are non-removable.

Answer 1

xt-1) Given: (x² - 4) (x-1) It is a sadional function. it is dis continuous wheree denominator equal to zero. for dis continuity (x² - 4) (0-1) = 0 » x² - 4=6 Dorl=0 4 x=1 ( Jake. Squadel) root x= 3 4 or + 2 or =) Hence at -2,1 g function is discontinuous. Jo classify. ANS factor numerator and denominator (22? 02 (362-(232) Carro a²b²= carb catb) (3-1) (3+1) (3-2)(3+2)(x-1) 17 (2-1)(x + 1) (00² + 1) (-1)(+2) (3-2)

(X4) (0+1) (0+1) (xal) (x+2) (2-2) (2-1) is common factor both numerador of & denominator. so at xall, it is eelmorable fino a (oct (3e2+1) if 27 L. (2+2) (x-2) (842) & Card) are not common in numerator and denominator, so at and x = -2. frx) has non-removable discontinuities. at X = 1 (removable) at x = 2 and a=-2 (non-elmovable) ANS