Let Consider the following two statements:

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Solution

Q.
Let $f (x) = \lim_{θ \to 0} (\frac{\cos (π x) - x^{(\frac{2}{θ})} \sin (x - 1)}{1 + x^{(\frac{2}{θ})} (x - 1)}), x \in ℝ .$

Consider the following two statements:

I. f(x) is discontinuous at x = 1

II. f(x) is continuous at x = -1

Then, [2026]

1 Only (I) is True

2 Only (II) is True

3 Neither (I) nor (II) is True

4 Both (I) and (II) are True

Ans.
(3)

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