Let f : R → R be a function given by f ( x ) = ⎩ ⎨ ⎧ x 2 1 − c o s 2 x , α , x β 1 − c o s x , x 0 where α , β ∈ R . If f is continuous at x = 0 , then α 2 + β 2 is equal t

Question

Let f : R → R be a function given by f ( x ) = ⎩ ⎨ ⎧ ​ x 2 1 − c o s 2 x ​ , α , x β 1 − c o s x ​ ​ , ​ x < 0 x = 0 , x > 0 ​ where α , β ∈ R . If f is continuous at x = 0 , then α 2 + β 2 is equal to :

TestHub · Accepted Answer

​ f ( 0 − ) = x → 0 − lim ​ x 2 2 sin 2 x ​ = 2 = α f ( 0 + ) = x → 0 + lim ​ β × 2 ​ 2 2 x ​ sin 2 x ​ ​ = 2 ​ β ​ = 2 ⇒ β = 2 2 ​ α 2 + β 2 = 4 + 8 = 12 ​

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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