Q11Multiple correct3 Marks1 Sep 2024Consider the following function f(x)f(x)f(x): f(x)={x(x+1)(x+2),if x≥11x−5,if x<1f(x) = \begin{cases} \frac{x}{(x+1)(x+2)}, & \text{if } x \ge 1 \\ \frac{1}{x-5}, & \text{if } x < 1 \end{cases}f(x)={(x+1)(x+2)x,x−51,if x≥1if x<1 Which of the following options is (are) correct?Alimx→−2+f′(x)=∞\lim_{x \to -2^+} f'(x) = \inftylimx→−2+f′(x)=∞BThe function fff is continuous.Climx→5−f(x)=limx→5+f(x)=542\lim_{x \to 5^-} f(x) = \lim_{x \to 5^+} f(x) = \frac{5}{42}limx→5−f(x)=limx→5+f(x)=425DAt x=1x = 1x=1, the function fff is discontinuous.
