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MCQMediumJEE Main 2026 · 28 January, Shift 2Continuity

Mathematics Question from JEE Main 2026 · 28 January, Shift 2

Let f(x)=lim⁡θ→0cos⁡πx−x2/θ sin⁡(x−1)1+x2/θ(x−1),x∈R.f(x)=\lim_{\theta\to 0} \frac{\cos \pi x-x^{2/\theta}\,\sin(x-1)} {1+x^{2/\theta}(x-1)},\qquad x\in\mathbb{R}. Consider the following statements:

[(I)] f(x)f(x) is discontinuous at x=1x=1. [(II)] f(x)f(x) is continuous at x=−1x=-1.

Then:

  • A

    Only (I) is true

  • B

    Neither (I) nor (II) is true

  • C

    Both (I) and (II) are true

  • D

    Only (II) is true

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