If limx→∞ x+cx−cx=4, then the value of c is

A
$\log_{10} 2$
B
$\log_{c} 2$
C
2
D
none of these

Solution:

We have,

$\begin{array}{l} lim_{x \to \infty} {(\frac{x + c}{x - c})}^{x} = 4 \\ \Rightarrow lim_{x \to \infty} {(1 + \frac{2 c}{x - c})}^{x} = 4 \\ = e^{lim_{x \to \infty} \frac{2 c x}{x - c}} = 4 \Rightarrow e^{2 c} = 4 \Rightarrow e^{c} = 2 \Rightarrow c = \log_{e} 2 \end{array}$

If $lim_{x \to \infty} {(\frac{x + c}{x - c})}^{x} = 4,$ then the value of $c$ is

Solution:

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