2. After finding the domain, roots, monotonicity and concavity intervals, the critical and inflection points (if any), asymptotes (vertical, horizontal or oblique if any) and limits at the edges of the domain, finally plot the following functions: a) $f (x) = \frac{2 x}{x ^{2} + 1}$ b) $f (x) = \frac{x ^{2} + 2 x + 1}{x}$ c) $f (x) = x ln x$ d) $f (x) = x^{2} + 1$ e) $f (x) = e^{? x^{2}}$ f) $f (x) = x^{3} + x^{2} ? 2 x$

Question

2. After finding the domain, roots, monotonicity and concavity intervals, the critical and inflection points (if any), asymptotes (vertical, horizontal or oblique if any) and limits at the edges of the domain, finally plot the following functions: a)

f (x) = \frac{2 x}{x ^{2} + 1}

b)

f (x) = \frac{x ^{2} + 2 x + 1}{x}

c)

f (x) = x ln x

d)

f (x) = x^{2} + 1

e)

f (x) = e^{? x^{2}}

f)

f (x) = x^{3} + x^{2} ? 2 x

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