_ x 0⁺ x ⁻¹ ( 2 x 1+x^2 ) ⁻¹ ( 1-x^2 1+x^2 ) ⁻¹ ( 3 x-x^3 1-3 x^2 ) is equal to

Step-by-step solution

_ x 0⁺ x ⁻¹ ( 2 x 1+x^2 ) ⁻¹ ( 1-x^2 1+x^2 ) ⁻¹ ( 3 x-x^3 1-3 x^2 ) We know that x 0⁺ aligned & 2 ⁻¹ x= ⁻¹ 2 x 1+x^2 = ⁻¹ ( 1-x^2 1+x^2 ) & 3 ⁻¹ x= ⁻¹ ( 3 x-x^3 1-3 x^2 ) aligned Limit becomes _ x 0⁺ x (2 ⁻¹ x ) (2 ⁻¹ x ) (3 ⁻¹ x ) _ x 0⁺ x 3 ⁻¹ x Using L Hospital rule _ x 0⁺ = 1 3 1 1+x^2 = 1 3 ( 1 1+0 ) = 1 3