Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Analysis Continuity & Differentiability
Let gn (x) = \(\frac{n x}{1+n^2 x^2}\), x ∈ [0, ∞). Which of the following is true as n → ∞ ?
1
gn → 0 pointwise but not uniformly
2
gn → 0 uniformly
3
gn(x) → x ∀x ∈ [0, ∞)
4
gn(x) → \(\frac{x}{1+x^2}\), ∀x ∈ [0, ∞)