Define f(x)= cases x, & x<0

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Define f(x)={sin⁡x,x<0,ax+b,0≤x<π,cos⁡x,x≥π.f(x)=\begin{cases}\sin x, & x<0,\\ ax+b, & 0\le x<\pi,\\ \cos x, & x\ge \pi.\end{cases} Which ordered pair (a,b)(a,b) ensures that ff is continuous for all real xx? (a) a=0,  b=0a=0,\;b=0 (b) a=1π,  b=0a=\dfrac1\pi,\;b=0 (c) a=−1π,  b=0a=-\dfrac1\pi,\;b=0 (d) a=−2π,  b=1a=-\dfrac2\pi,\;b=1

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