What is the limit as x approaches-infinity of (11x+6)/(4-6x) ?

The limit as x approaches-infinity of (11x+6)/(4-6x) is -11/6

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limit as x approaches-infinity of (11x+6)/(4-6x)

x \to - \infty lim (\frac{11 x + 6}{4 - 6 x})

- \frac{11}{6}

Decimal

- 1.83333 \dots

Solution steps

x \to - \infty lim (\frac{11 x + 6}{4 - 6 x})

Divide by highest denominator power:

\frac{11 + \frac{6}{x}}{\frac{4}{x} - 6}

= x \to - \infty lim (\frac{11 + \frac{6}{x}}{\frac{4}{x} - 6})

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} ( 11 + \frac{6}{x} )}{lim _{x \to - \infty} ( \frac{4}{x} - 6 )}

x \to - \infty lim (11 + \frac{6}{x}) = 11

x \to - \infty lim (\frac{4}{x} - 6) = - 6

= \frac{11}{- 6}

Simplify

= - \frac{11}{6}

x = e^{2 y}, y = 0, x = e^{4}

y = x^{2}, y = 5

\frac{d}{d x} (11 cos (x))

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

\frac{d}{d x} (2 x + e^{x})

What is the limit as x approaches-infinity of (11x+6)/(4-6x) ?
The limit as x approaches-infinity of (11x+6)/(4-6x) is -11/6