Let [t] denote the greatest integer less than or equal to t. If the function f(x)={\\begin{array}{c}b^2 \sin \\ (\\\{\pi\end\frac{array}{2} [\frac{\pi}{2}(\cos x+ \sin x) \cos x] ) {, } , x< 0 ; \binom{ \sin x-\frac{1}{2} \sin 2 x}/{x^3} ,{, } x>0 ; a ,{, } x=0 } is continuous at x=0, then a^2+b^2 is equal to: [24 Jan 2026 Shift 2]

Limits, Continuity and Differentiability Part 3

Section: Mathematics

Question : 4 of 69

Marks: +1, -0

Let [t] denote the greatest integer less than or equal to t. If the function f(x)={

b2sin‌(‌

[‌

(cos‌x+sin‌x)‌cos‌x]),‌

x<0

‌

sin‌x−

sin‌2x

,‌x>0

,‌x=0

is continuous at x=0, then a2+b2 is equal to:

[24 Jan 2026 Shift 2]

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