What is the limit as x approaches-infinity of (sqrt(x^2+4))/(x+7) ?

The limit as x approaches-infinity of (sqrt(x^2+4))/(x+7) is -1

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limit as x approaches-infinity of (sqrt(x^2+4))/(x+7)

x \to - \infty lim (\frac{x ^{2} + 4}{x + 7})

- 1

Solution steps

x \to - \infty lim (\frac{x ^{2} + 4}{x + 7})

Divide by highest denominator power:

\frac{\frac{x ^{2} + 4}{x}}{1 + \frac{7}{x}}

= x \to - \infty lim (\frac{\frac{x ^{2} + 4}{x}}{1 + \frac{7}{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} ( \frac{x ^{2} + 4}{x} )}{lim _{x \to - \infty} ( 1 + \frac{7}{x} )}

x \to - \infty lim (\frac{x ^{2} + 4}{x}) = - 1

x \to - \infty lim (1 + \frac{7}{x}) = 1

= \frac{- 1}{1}

Simplify

= - 1

x \to 2 lim (\frac{x ^{2} + x - 6}{x ^{3} - 9 x})

x \to 0 lim (1 - cos (6 x))

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

x \to \infty lim (5 x - x^{2})

n \to \infty lim (\frac{ln ( n + 2 )}{ln ( n + 1 )})

What is the limit as x approaches-infinity of (sqrt(x^2+4))/(x+7) ?
The limit as x approaches-infinity of (sqrt(x^2+4))/(x+7) is -1