Determine the limit, or show it doesn't exist: \lim_{x\to 2}

Arely Briggs

Arely Briggs

Answered question

2022-01-28

Determine the limit, or show it doesn't exist: limx2(arctan(12x))2

Answer & Explanation

Sean Becker

Sean Becker

Beginner2022-01-29Added 16 answers

Performing the substitution u=12x, this is just limu(tan1u)2 which evaluates to π24, since limutan1u=π2. (Note that there actually is a slight technicality, namely that we took only the right hand limit of the original integral. Luckily, the fact that the arctan is squared makes the left hand limit consistent.)
hmotans

hmotans

Beginner2022-01-30Added 8 answers

Intuitively, as x 2 from the positive side, 12x approaches and as x approaches 2 from the negative side, 12x approaches . However, arctan of ±  is  ±π2, so squaring this gets π24, the value of the limit.
Just because, lets

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