Question

Discuss the continuity of the function f(x) at x = 1, where f(x) = lim_{(n → ∞)}((cos(πx) - x²ⁿsin(x - 1))/(1 + x^{2n + 1} + (-x²ⁿ)))

Answer 1

Case-I: When x < 1

Case-II: When x > 1

We have f(x) 

= lim _(x→1⁺) (– sin(x – 1)/(x – 1)) = – 1

Thus, f(x) is continuous at x = 1.