What is the limit as x approaches infinity of (arcsec(x))/(sqrt(x)) ?

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limit as x approaches infinity of (arcsec(x))/(sqrt(x))

x \to \infty lim (\frac{arcsec ( x )}{x})

0

Solution steps

x \to \infty lim (\frac{arcsec ( x )}{x})

x \to a lim [\frac{f ( x )}{g ( x )}] = \frac{lim _{x \to a} f ( x )}{lim _{x \to a} g ( x )}, x \to a lim g (x) \neq = 0

With the exception of indeterminate form

= \frac{lim _{x \to \infty} ( arcsec ( x ) )}{lim _{x \to \infty} ( x )}

x \to \infty lim (arcsec (x)) = \frac{π}{2}

x \to \infty lim (x) = \infty

= \frac{\frac{π}{2}}{\infty}

Apply Infinity Property:

\frac{c}{\infty} = 0

= 0

t \to 0 lim (\frac{cos ( t )}{t})

x \to 1 + lim (e^{\frac{( - x ^{2} )}{3 ( x - 1 )}})

x \to 0 - lim (\frac{∣ x ∣}{- 2 x})

x \to 0 lim (ln (1 - x^{2}))

x \to 1 lim (\frac{x ^{\frac{1}{4}} - 1}{x ^{\frac{1}{3}} - 1})

What is the limit as x approaches infinity of (arcsec(x))/(sqrt(x)) ?
The limit as x approaches infinity of (arcsec(x))/(sqrt(x)) is 0