Let f : R→[0, ∞) be such that limx→5 f(x) exists and limx→5 (f(x))2−9|x−5|=0. Then, limx→5 f(x) equals
1
2
3
0
limx→5 (f(x))2−9|x−5|=0⇒ limx→5 (f(x))2−9=0
⇒ l2-9=0, where limx→5 f(x)=l
⇒ l=±3
⇒ l=3 [∴ f(x)≥0 for all x ∈ R]
⇒ limx→5 f(x)=3