To determine

To find: Find the limit limx→∞⁡ln⁡1+x2-ln⁡(1+x)

Answer

The limit is ∞.

Explanation

Calculation:

We have to find the limit limx→∞⁡ln⁡1+x2-ln⁡(1+x).

We use the formula

ln⁡a-ln⁡b=ln⁡ab

So, ln⁡1+x2-ln⁡(1+x)=ln⁡(1+x2)(1+x)=ln⁡x1+1x21+1x. So

limx→∞⁡ln⁡1+x2-ln⁡1+x=limx→∞ln⁡x1+1x21+1x=limx→∞ln⁡x1+1x2-limx→∞ln⁡1+1x

=limx→∞ ln∞-limx→∞ln⁡1=∞-0=∞

Conclusion:

The limit is ∞.