Question 15 (CSIR NET June 2019)

Let $g_n(x) = \frac{nx}{1+n^2x^2}$, $x \in [0, \infty)$, let $n \to \infty$, then-

(a) $g_n \to 0$ pointwise but not uniformly.

(b) $g_n \to 0$ uniformly

(c) $g_n \to x$ for all $x \in [0, \infty)$

(d) $g_n \to \frac{x}{1+x^2}$ for all $x \in [0, \infty)$


Explanation: (a) is correct.

Dr. Pawan

Hi, I am Dr. Math.

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