Answer Happy

(a) What is wrong with the following equation? x−4x2+x−20​=x+5(x−4)(x+5)=x2+x−20​ 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=4, 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. x→4lim​x−4x2+x−20​=x→4lim​(x+5) Since x−4x2+x−20​ and x+5 are both continuous, the equation follows. Since the equation holds for all x=4, it follows that both sides of the equation approach the same limit as x→4. This equation follows from the fact that the equation in part (a) is correct. None of these − the equation is not correct.