What is the limit as x approaches 0 of sqrt(3+arctan(1/x)) ?

The limit as x approaches 0 of sqrt(3+arctan(1/x)) is diverges

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limit as x approaches 0 of sqrt(3+arctan(1/x))

x \to 0 lim (3 + arctan (\frac{1}{x}))

diverges

Solution steps

x \to 0 lim (3 + arctan (\frac{1}{x}))

x \to a - lim f (x) \neq = x \to a + lim f (x)

then the limit does not exist

x \to 0 + lim (3 + arctan (\frac{1}{x})) = 3 + \frac{π}{2}

x \to 0 - lim (3 + arctan (\frac{1}{x})) = 3 - \frac{π}{2}

= diverges

x \to 0 lim (\frac{5}{x ^{2} - x} + \frac{5}{x})

x \to 7 lim (- 3 ln (e^{x}))

x \to - 1 - lim (x^{2} + a)

x \to \infty lim (\frac{2}{x} + 3)

x \to \infty lim ((1 + a x)^{\frac{b}{x}})

What is the limit as x approaches 0 of sqrt(3+arctan(1/x)) ?
The limit as x approaches 0 of sqrt(3+arctan(1/x)) is diverges