If f x = s i n a + 2 x + s i n x x ; x 0 b ; x = 0 x + 3 x 2 1 / 3 - x 1 / 3 x 1 / 3 ; x 0 is continuous at x = 0 , then a + 2 b is equal to:

Question

If f x = s i n a + 2 x + s i n x x ; x 0 b ; x = 0 x + 3 x 2 1 / 3 - x 1 / 3 x 1 / 3 ; x > 0 is continuous at x = 0 , then a + 2 b is equal to:, 1, - 1, 0, - 2

MARKS App · Accepted Answer

f 0 - = lim x → 0 - sin a x cos 2 x x + sin 2 x cos a x x + sin x x = lim x → 0 - a cos 2 x + 2 cos a x + 1 = a + 3 Also, f 0 = b f 0 + = lim x → 0 x 1 3 x 1 3 1 + 3 x 1 3 - 1 x , this is 0 0 form Apply LH Rule ⇒ f 0 + = 1 ∴ a = - 2 b = 1 ∴ a + 2 b = 0

Search any question & find its solution

Looking for more such questions to practice?