Mathematics

Mathematics

Problem

Consider f(x)=lim⁡n→∞xn+1−sin⁡xnxn+sin⁡xnf(x) = \lim_{n \to \infty} \frac{x^{n+1} - \sin x^n}{x^n + \sin x^n} for x>0,x≠1,f(1)=0x > 0, x \neq 1, f(1) = 0 then a. ff is continuous at x=1x = 1 b. ff has a finite discontinuity at x=1x = 1 c. ff has an infinite or oscillatory discontinuity at x=1x = 1 d. ff has a removal type of discontinuity at x=1x = 1

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