Let f ( x ) = sin x and g ( x ) = x . Statement 1: f ( x ) ⩽ g ( x ) for x ∈ ( 0 , ∞ ) . Statement 2: f ( x ) ≤ 1 for x ∈ ( 0 , ∞ ) , but g ( x ) → ∞ as x → ∞ .

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Let f ( x ) = sin x and g ( x ) = x Statement-1: f ( x ) ≤ g x ( ∀ x ) ∈ 0 , ∞ ( ) i.e., sin x ≤ x ∀ x ∈ ( 0 , ∞ ) which is true Statement-2: f ( x ) ≤ 1∀ x ∈ 0 , ∞ ( ) i.e., sin x ≤ 1∀ x ∈ ( 0 , ∞ ) It is true and g ( x ) = x → ∞ as x → ∞ also true.

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