Let f(x)=\lim_{\theta \rightarrow 0} (\binom{\cos \pi x-x x^{ (\frac{2}{\theta}) } \sin (x-1)}/{1+x^{ (\frac{2}{\theta}) }(x-1)}) , x \in R. Consider the following two statements : (I) f(x) is discontinuous at x=1. (II) f(x) is continuous at x=-1. Then, [28 Jan 2026 Shift 2]

Correct Answer is : Neither (I) nor (II) is True

Limits, Continuity and Differentiability Part 3

Section: Mathematics

Question : 1 of 69

Marks: +1, -0

Let f(x)=

lim

θ⟶0

(‌

cos‌π‌x−xx(

)sin‌(x−1)

1+x(‌

)(x−1)

),x∈R. Consider the following two statements :
(I) f(x) is discontinuous at x=1.
(II) f(x) is continuous at x=−1.
Then,

[28 Jan 2026 Shift 2]

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