Assume that limθ→−1 f(θ)exists and θ2+θ−2θ+3≤f(θ)θ2≤θ2+2θ−1θ+3holds for certain interval containing the point θ=-1, then   limθ→−1 f(θ)θ2 , is 

Assume that limθ1f(θ)exists and θ2+θ2θ+3f(θ)θ2θ2+2θ1θ+3holds for certain interval containing the point θ=-1, then   limθ1f(θ)θ2 , is 

  1. A

    equal to f(-1)

  2. B

    equal to 1

  3. C

    non-existent

  4. D

    equal to  -1 

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    Solution:

    We have,  

    limθ1θ2+θ2θ+3=1 and limθ1θ2+2θ1θ+3=-1

     θ2+θ2θ+3f(θ)θ2θ2+2θ1θ+3limθ1f(θ)θ2=1

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