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If F(x) is defined in x in (-1/3,1/3) ...

If F(x) is defined in `x in (-1/3,1/3)`
f(x) = `{((1/x)log_e((1+3x)/(1-2x)),x !=0),(k,x=0):} ` find k such that f(x) is continuous

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To find the value of \( k \) such that the function \( f(x) \) is continuous at \( x = 0 \), we need to ensure that the limit of \( f(x) \) as \( x \) approaches 0 is equal to \( f(0) \). The function is defined as follows: \[ f(x) = \begin{cases} \frac{1}{x} \log_e \left( \frac{1 + 3x}{1 - 2x} \right) & \text{if } x \neq 0 \\ k & \text{if } x = 0 ...
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