What is the limit as x approaches infinity of (2(x-8)^{35})/((x-1)^{35)} ?

The limit as x approaches infinity of (2(x-8)^{35})/((x-1)^{35)} is 2

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limit as x approaches infinity of (2(x-8)^{35})/((x-1)^{35)}

x \to \infty lim (\frac{2 ( x - 8 ) ^{35}}{( x - 1 ) ^{35}})

2

Solution steps

x \to \infty lim (\frac{2 ( x - 8 ) ^{35}}{( x - 1 ) ^{35}})

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

= 2 \cdot x \to \infty lim (\frac{( x - 8 ) ^{35}}{( x - 1 ) ^{35}})

Apply the following algebraic property

: a + b = a (1 + \frac{b}{a})

\frac{( x - 8 ) ^{35}}{( x - 1 ) ^{35}} = \frac{( x ( 1 - \frac{8}{x} ) ) ^{35}}{( x ( 1 - \frac{1}{x} ) ) ^{35}}

= 2 \cdot x \to \infty lim (\frac{( x ( 1 - \frac{8}{x} ) ) ^{35}}{( x ( 1 - \frac{1}{x} ) ) ^{35}})

Simplify

\frac{( x ( 1 - \frac{8}{x} ) ) ^{35}}{( x ( 1 - \frac{1}{x} ) ) ^{35}} : \frac{( 1 - \frac{8}{x} ) ^{35}}{( 1 - \frac{1}{x} ) ^{35}}

= 2 \cdot x \to \infty lim (\frac{( 1 - \frac{8}{x} ) ^{35}}{( 1 - \frac{1}{x} ) ^{35}})

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

= 2 \cdot \frac{lim _{x \to \infty} ( ( 1 - \frac{8}{x} ) ^{35} )}{lim _{x \to \infty} ( ( 1 - \frac{1}{x} ) ^{35} )}

x \to \infty lim ((1 - \frac{8}{x})^{35}) = 1

x \to \infty lim ((1 - \frac{1}{x})^{35}) = 1

= 2 \cdot \frac{1}{1}

Simplify

= 2

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

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\frac{d}{d x} (\frac{432}{x})

\int \frac{4 x ^{2} - 7 x - 12}{x ( x + 2 ) ( x - 3 )} d x

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What is the limit as x approaches infinity of (2(x-8)^{35})/((x-1)^{35)} ?
The limit as x approaches infinity of (2(x-8)^{35})/((x-1)^{35)} is 2