First slide

Introduction to limits

Question

Let f be continuous function on R such that $f (\frac{1}{4 n}) = \sin (e^{n}) e^{- n^{2}} + \frac{n^{2}}{n^{2} + 1} .$ Then the value of f(0) is

Moderate

Solution

$f (0) = \underset{x \to 0}{^{L t}} f (x) = \underset{n \to \infty}{^{L t}} f (\frac{1}{4 n}) = 0 + 1 = 1$

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