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BITSAT2017MathematicsApplication of DerivativesActual

If the curve y = a x and y = b x intersect at angle α , then tan α is equal to

Options

  1. Aa - b 1 + a b
  2. Blog a - log b 1 + log a log b
  3. Ca + b 1 - a b
  4. Dlog a + log b 1 - log a log b

Correct answer

B. log a - log b 1 + log a log b

Step-by-step solution

Clearly, the point of intersection of curves is ( 0 , 1 ) . Now, slope of tangent of first curve m 1 = d y d x = a x log a ⇒ d y d x ( 0 , 1 ) = m 1 = log a Slope of tangent of second curve, m 2 = d y d x = b x log b ⇒    m 2 = d y d x ( 0 , 1 ) = log b ∴   tan α = m 1 - m 2 1 + m 1 m 2 = log a - log b 1 + log a log b

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