What is the limit as x approaches-infinity of (4-7x)/(2+3x) ?

The limit as x approaches-infinity of (4-7x)/(2+3x) is -7/3

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limit as x approaches-infinity of (4-7x)/(2+3x)

x \to - \infty lim (\frac{4 - 7 x}{2 + 3 x})

- \frac{7}{3}

Decimal Notation

- 2.33333 \dots

Solution steps

x \to - \infty lim (\frac{4 - 7 x}{2 + 3 x})

Divide by highest denominator power:

\frac{\frac{4}{x} - 7}{\frac{2}{x} + 3}

= x \to - \infty lim (\frac{\frac{4}{x} - 7}{\frac{2}{x} + 3})

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{4}{x} - 7 )}{lim _{x \to - \infty} ( \frac{2}{x} + 3 )}

x \to - \infty lim (\frac{4}{x} - 7) = - 7

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

= \frac{- 7}{3}

Simplify

= - \frac{7}{3}

\frac{\partial}{\partial y} (x ln (x) + y ln (x))

\int \frac{1}{b - a y} d y

\int (x^{2} - 4 x + 5) d x

4 + 3 x

\frac{d}{d x} (arcsin (\frac{x}{10}))

What is the limit as x approaches-infinity of (4-7x)/(2+3x) ?
The limit as x approaches-infinity of (4-7x)/(2+3x) is -7/3