First slide

Continuity

Question

$Number if points of non-differentiability of the function$
$g (x) = [x^{2}] \{\cos^{2} 4 x\} + \{x^{2}\} [\cos^{2} 4 x] + x^{2} \sin^{2} 4 x + [x^{2}] [\cos^{2} 4 x] + \{x^{2}\} \{\cos^{2} 4 x\} in (- 50, 50)$
$where [x] and {x} denotes the g.I.F and fractional point function of x respectively is equal to$

Moderate

Solution

$([x^{2}] + \{x^{2}\}) (\{\cos^{2} 4 x\} + [\cos^{2} 4 x]) + x^{2} \sin^{2} 4 x$
$\begin{array}{l} = x^{2} \cos^{2} 4 x + x^{2} \sin^{2} 4 x \\ = x^{2} \end{array}$
$Clearly g (x) is continuous and differentiable \forall x \in R$
Number of points of non-differentiability in ‘0’

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