MHT CET20192 May 2019Morning ShiftMathematicsContinuity and DifferentiabilityActual

If the function f x = log ⁡ 1 + a x - log ⁡ 1 - b x x , x ≠ 0 is continuous at x = 0 then, f 0 = ________

Options

Alog ⁡ a - log ⁡ b
Ba + b
Clog ⁡ a + log ⁡ b
Da - b

Correct answer

B. a + b

Step-by-step solution

Given: f x = l o g 1 + a x - l o g 1 - b x x x ≠ 0 is continuous at x = 0 , then f 0 = l i m x → 0 log ⁡ 1 + a x - log ⁡ 1 - b x x , 0 0 form l i m x → 0 a 1 + a x + b 1 - b x 1 (by L–hospital rule) = a + b

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