Function Continuity at Points (Jee Mains)

Continuity and Differentiability

Medium

Function Continuity at Points

Let $f(x) = \mathop {\lim }\limits_{\theta \to 0} \left( {\frac{{\cos \pi x - {x^{\left( {\frac{2}{\theta }} \right)}}\sin (x - 1)}}{{1 + {x^{\left( {\frac{2}{\theta }} \right)}}(x - 1)}}} \right),x \in R$ .
Consider the following two statements :
(I) f(x) is discontinous at x = 1.
(II) f(x) is continous at x = –1.
Then,

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