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Problem $1$: Given f$($x$)=$ x$+2/$ x$^2+1$

Find lim x$->0^-$ f$($x$)$ and lim x$->0^+$ f$($x$)$ in three ways:

Numerical intuition $($what dominates the numerator and denominator$)$

Python $($see code snippets$)$

Desmos

Write a short description of the information contained in each approach and how they are different facets of the same limit$.$

Find lim x$->$infinity f$($x$)$ in three ways:

Numerical intuition $($what dominates the numerator and denominator$)$

Python $($see code snippets$)$

Desmos

Write a short description of the information contained in each approach and how they are different facets of the same limit$.$