Let denote the greatest integer less than or equal to . If the function is continuous at , then is equal to [2026]

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Solution

Q.
Let $[t]$ denote the greatest integer less than or equal to $t$ . If the function

$f (x) =$ ${\begin{matrix} b^{2} \sin (\frac{π}{2} [\frac{π}{2} (\cos x + \sin x) \cos x]), & x < 0 \\ \frac{\sin x - \frac{1}{2} \sin 2 x}{x^{3}}, & x > 0 \\ a, & x = 0 \end{matrix}$

is continuous at $x = 0$ , then $a^{2} + b^{2}$ is equal to [2026]

1 $\frac{9}{16}$

2 $\frac{1}{2}$

3 $\frac{5}{8}$

4 $\frac{3}{4}$

Ans.
(4)

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