Let a , b ∈ R , b ≠ 0 . Defined a function, f x = a sin π 2 ( x − 1 ) ,      for x ≤ 0 tan 2 x − sin 2 x b x 3 ,      for x > 0 If f is continuous at x = 0 , then 10 - a b is equal to

Step-by-step solution

We have, f x = a sin π 2 x − 1 ,      for   x ≤ 0 tan 2 x − sin 2 x b x 3 ,      for     x > 0 If function is continuous at x = 0 , then LHL = RHL = f 0 Now, LHL = lim x → 0 - a sin π 2 x − 1 ⇒ LHL = lim h → 0 a sin π 2 0 - h − 1 ⇒ LHL = lim h → 0 a sin π 2 − 1 ⇒ LHL = - a Now, RHL = lim x → 0 +   tan 2 x − sin 2 x b x 3 ∵ sin x = x &#