For α , β , γ , ∈ R , if lim x → 0 s i n 2 x − β x x 2 s i n αx + ( γ − 1 ) e x 2 = 3 , then β + γ − α is equal to:

Question

For α , β , γ , ∈ R , if lim x → 0 ​ s i n 2 x − β x x 2 s i n αx + ( γ − 1 ) e x 2 ​ = 3 , then β + γ − α is equal to:

TestHub · Accepted Answer

​ x → 10 lim ​ 2 x − 6 8 x 3 ​ − β x x 2 ( αx ) + ( γ − 1 ) ( 1 + 1 x 2 ​ ) ​ = 3 x → 0 lim ​ ( 2 − β ) x − 3 4 ​ x 3 ( γ − 1 ) + ( γ − 1 ) x 2 + α x 3 ​ = 3 γ − 1 , β = 2 , 4 − 3 α ​ = + 3 ⇒ α = − 4 β + γ − α = 7 ​

Mathematics - Limits Question with Solution | TestHub

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JEE Main (2028)