To determine
To find: Find the limit limx→∞ln1+x2-ln(1+x)
Answer
The limit is ∞.
Explanation
Calculation:
We have to find the limit limx→∞ln1+x2-ln(1+x).
We use the formula
lna-lnb=lnab
So, ln1+x2-ln(1+x)=ln(1+x2)(1+x)=lnx1+1x21+1x. So
limx→∞ln1+x2-ln1+x=limx→∞lnx1+1x21+1x=limx→∞lnx1+1x2-limx→∞ln1+1x
=limx→∞ ln∞-limx→∞ln1=∞-0=∞
Conclusion:
The limit is ∞.