The function f: R → R defined by f(x)= lim n → ∞ (cos (2 π x)-x²ⁿ sin (x-1))/(1+x²ⁿ⁺¹-x²ⁿ) is continuous for all x in:

Limit, Continuity and Differentiability: JEE Main 2022 Mathematics question

JEE Main 2022 · 28 Jul, Evening shift · Q4157

JEE Main 202228 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

The function

f: \mathbb{R} \rightarrow \mathbb{R}

defined by

f(x)=\lim\limits_{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}

is continuous for all x in :

JEE Main 2022 · 28 Jul, Evening shift · Q4157

JEE Main 202228 Jul, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

The function

f: \mathbb{R} \rightarrow \mathbb{R}

defined by

f(x)=\lim\limits_{n \rightarrow \infty} \frac{\cos (2 \pi x)-x^{2 n} \sin (x-1)}{1+x^{2 n+1}-x^{2 n}}

is continuous for all x in :