\( = \lim _ { x \rightarrow + ^ { + } } ( x ^ { 2 } - 2 \ln x + 2 ) = \)

To evaluate the limit \( \lim _ { x \rightarrow + ^ { + } } ( x ^ { 2 } - 2 \ln x + 2 ) \), let's analyze the expression. As \( x \to +\infty \), \( \ln x \) grows slower than \( x^2 \). Thus, \( 2 \ln x \) becomes insignificant compared to \( x^2 \). So, we can focus on the dominant term: \[ \lim _ { x \rightarrow + ^ { + } } ( x ^ { 2 } - 2 \ln x + 2 ) \approx \lim _ { x \rightarrow + ^ { + } } x^2 = +\infty. \] Now the limit diverges to \( + \infty \). Additionally, since \( ( x^2 + 2 - 2 \ln x ) \) involves both polynomial and logarithmic functions, keeping track of their growth rates provides insight into their interplay as \( x \) increases. The polynomial term \( x^2 \) will always overshadow the logarithmic term, leading us to ultimately determine that this limit indeed approaches infinity.