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Part of 2019 ISI Entrance Examination

Problems(1)

ISI 2019 : Problem #2

Source: I.S.I. 2019

5/5/2019
Let f:(0,∞)→Rf:(0,\infty)\to\mathbb{R} be defined by f(x)=lim⁡n→∞cos⁡n(1nx)f(x)=\lim_{n\to\infty}\cos^n\bigg(\frac{1}{n^x}\bigg) (a) Show that ff has exactly one point of discontinuity. (b) Evaluate ff at its point of discontinuity.
isiIndian Statistical Institute2019calculus