Question

prove that limit of x=2 , 3^x +3^3-x -12/ 3^3-x-3^x/2

Answer 1

Step-by-step explanation:

Note that (4+x−3x3)−2=−(3x3−x−2)=−(x−1)(3x2+3x+2)

So ∣∣(4+x−3x3)−2∣∣=|x−1|⋅∣∣3x2+3x+2∣∣

Given ε>0, let δ=min{1,ε20} and note that δ>0

If 0<|x−1|<1

then 0<x<2 so that 2<(3x2+3x+2)<20 and

∣∣3x2+3x+2∣∣<20

So, ∣∣(4+x−3x3)−2∣∣=|x−1|⋅∣∣3x