NTA Abhyas JEE Main2020MathematicsContinuity and DifferentiabilityPractice

If f x = s i n 2 x c x + x 4 x + a 2 - a ; x ≠ 0 , a < 0 , c ≠ 0 b ; x = 0 , b ≠ 0 and f x is continuous at x = 0 , then the value of b c is equal to

Correct answer

Step-by-step solution

∵ f x is continuous at x = 0 ∴ l i m x → 0 f x = f 0 l i m x → 0 sin ⁡ 2 x c x + x 4 x + a 2 - a x + a 2 + a x + a 2 + a = b l i m x → 0 2 c + x x + a 2 + a 4 x + a 2 - a 2 = b ⇒ 2 c + 0 = b     ( as   a < 0 ) ⇒ b c = 2

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