_ x 0 a^x-b^x x is equal to

Step-by-step solution

The given limit is _ x 0 a^x - b^x x . Rewrite the expression by adding and subtracting 1 in the numerator: _ x 0 (a^x - 1) - (b^x - 1) x Using the property of limits, this can be split into two separate limits: _ x 0 a^x - 1 x - _ x 0 b^x - 1 x Recall the standard limit formula _ x 0 k^x - 1 x = k . Applying this formula to both terms: a - b Using the logarithmic property a - b = ( a b ) , the result is ( a b ) . Answer: a b