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

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

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

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

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

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

x \to a lim [c \cdot f (x)] = c \cdot x \to a lim f (x)

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

Divide by highest denominator power:

\frac{1}{3 - \frac{2}{x}}

= 4 \cdot x \to \infty lim (\frac{1}{3 - \frac{2}{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

= 4 \cdot \frac{lim _{x \to \infty} ( 1 )}{lim _{x \to \infty} ( 3 - \frac{2}{x} )}

x \to \infty lim (1) = 1

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

= 4 \cdot \frac{1}{3}

Simplify

4 \cdot \frac{1}{3} : \frac{4}{3}

= \frac{4}{3}

x \to 0 lim (\frac{( 2 ^{x} - 5 ^{x} )}{x})

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

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

n \to \infty lim (n (1 + 2^{n} + 3^{n}))

h \to 0 lim (\frac{( 3 - 9 + h )}{h})

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