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Maths-

General

Easy

Question

Given that log_px = α and log_qx = β, then value of log_p_/q x equals-

$\frac{α β}{β - α}$
$\frac{β - α}{α β}$
$\frac{α - β}{α β}$
$\frac{α β}{α - β}$

The correct answer is: $fraction numerator alpha beta over denominator beta minus alpha end fraction$

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If f(x) is the primitive of $fraction numerator sin invisible function application root index 3 of x end root log invisible function application left parenthesis 1 plus 3 x right parenthesis over denominator left parenthesis tan to the power of – 1 end exponent invisible function application square root of x right parenthesis to the power of 2 end exponent left parenthesis e to the power of root index 3 of x end root end exponent – 1 right parenthesis end fraction$ (x $not equal to$ 0), then $stack l i m with x rightwards arrow 0 below$ f ' (x) is -

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