What is the limit as x approaches infinity of (4x-5)/(2x+3) ?

The limit as x approaches infinity of (4x-5)/(2x+3) is 2

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limit as x approaches infinity of (4x-5)/(2x+3)

x \to \infty lim (\frac{4 x - 5}{2 x + 3})

2

Solution steps

x \to \infty lim (\frac{4 x - 5}{2 x + 3})

Divide by highest denominator power:

\frac{4 - \frac{5}{x}}{2 + \frac{3}{x}}

= x \to \infty lim (\frac{4 - \frac{5}{x}}{2 + \frac{3}{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} ( 4 - \frac{5}{x} )}{lim _{x \to \infty} ( 2 + \frac{3}{x} )}

x \to \infty lim (4 - \frac{5}{x}) = 4

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

= \frac{4}{2}

Simplify

= 2

n = 1 \sum \infty \frac{4 n}{4 n + 7}

(2 x + 5) (4 x - 5)^{2}

\frac{d}{d x} (ln (x^{s i n (x)}))

\int \frac{1}{x 9 x - 1} d x

\int (\frac{cos ( x )}{sin ( 2 x )}) d x

What is the limit as x approaches infinity of (4x-5)/(2x+3) ?
The limit as x approaches infinity of (4x-5)/(2x+3) is 2