The correct option is B a/b The value of lim _ x⟶∞ #160; ax + b bx + a #160; is =lim _ x⟶∞ #160; x ( a + b / x ) x +( b + a / x ) ...

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Limit

x→∞limax+b/bx...

Question

$lim x \to \infty \frac{a x + b}{b x + a} =$

\frac{a + b}{b + a}

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\frac{a}{b}

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\frac{b}{a}

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\frac{a b}{b a}

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Solution

The correct option is B $\frac{a}{b}$
The value of ${lim}_{x ⟶ \infty} \frac{a x + b}{b x + a}$ is
$= lim x ⟶ \infty \frac{x (a + \frac{b}{x})}{x + (b + \frac{a}{x})}$

$= lim x ⟶ \infty \frac{a + \frac{b}{x}}{b + \frac{a}{x}}$

$= \frac{a}{b}$ .... We know $lim x ⟶ \infty \frac{1}{x} = 0$

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