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( a ) What is wrong with the following equation? x 2 + x - 6 x - 2 = x + 3 ( x

(a) What is wrong with the following equation? x2+x-6x-2=x+3(x-2)(x+3)x2+x-6 The left-hand side is not defined for x=0, but the right-hand side is. The left-hand side is not defined for x=2, but the right-hand side is. None of these - the equation is correct. (b) In view of part (a), explain why the following equation is correct. limx2x2+x-6x-2=limx2(x+3) Since x2+x-6x-2 and x+3 are both continuous, the equation follows. Since the equation holds for all x2, it follows that both sides of the equation approach the same limit as x2. This equation

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