What is the limit as x approaches infinity of (((2x-3))/((2x+5)))^{2x+1} ?

The limit as x approaches infinity of (((2x-3))/((2x+5)))^{2x+1} is 1/(e^8)

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limit as x approaches infinity of (((2x-3))/((2x+5)))^{2x+1}

x \to \infty lim ((\frac{( 2 x - 3 )}{( 2 x + 5 )})^{2 x + 1})

\frac{1}{e ^{8}}

Decimal Notation

0.00033 \dots

Solution steps

x \to \infty lim ((\frac{2 x - 3}{2 x + 5})^{2 x + 1})

Simplify

(\frac{2 x - 3}{2 x + 5})^{2 x + 1} : (\frac{2 x - 3}{2 x + 5})^{2 x} \frac{2 x - 3}{2 x + 5}

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

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

With the exception of indeterminate form

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

x \to \infty lim ((\frac{2 x - 3}{2 x + 5})^{2 x}) = \frac{1}{e ^{8}}

x \to \infty lim (\frac{2 x - 3}{2 x + 5}) = 1

= \frac{1}{e ^{8}} \cdot 1

Simplify

= \frac{1}{e ^{8}}

x = \frac{4}{y}, x = \frac{y}{8}, x = 8 y

\frac{\partial}{\partial x} (\frac{3 x + t}{x - 5 t})

\int_{1}^{2} (8 x^{3} + 3 x^{2}) d x

\frac{d}{d x} (\frac{x ^{3}}{3} - x)

n = 2 \sum \infty - (\frac{2}{3})^{n}

What is the limit as x approaches infinity of (((2x-3))/((2x+5)))^{2x+1} ?
The limit as x approaches infinity of (((2x-3))/((2x+5)))^{2x+1} is 1/(e^8)