If l=limx→−2 tan⁡πxx+2+limx→∞ 1+1x2xthen which one of the following is not correct?

We have,l=limx→−2 tan⁡πxx+2+limx→∞ 1+1x2x⇒ l=limx→−2 tan⁡(2π+πx)x+2+limx→∞ 1+1x2x⇒ l=πlimx→−2 tan⁡π(x+2)π(x+2)+elimx→∞ xx2=π+e0=π+1 So, option (c) is incorrect.