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Question Number 87799 by M±th+et£s last updated on 06/Apr/20

$$f\left(x\right)=\{\begin{array}{l}{ax}^2+bx-1⩽x⩽0\\ {cx}^2+d0<x⩽\frac{1}{2}\\ bx+d\frac{1}{2}<x⩽1\end{array}$$$$f\left(x\right)iscontinuouson[-1,1]$$$$proved=0$$$$c=2b$$

Commented by john santu last updated on 06/Apr/20

$$\underset{x\to 0^{-}}{\lim }\mathrm{f}\left(\mathrm{x}\right)=\underset{x\to 0^{+}}{\lim }\mathrm{f}\left(\mathrm{x}\right)$$$$\underset{x\to 0^{-}}{\lim }({\mathrm{ax}}^2+\mathrm{bx})\underset{x\to 0^{+}}{\lim }({\mathrm{cx}}^2+\mathrm{d})$$$$0=\mathrm{d}$$$$\underset{x\to 0.5^{-}}{\lim }({\mathrm{cx}}^2+\mathrm{d})=\underset{x\to 0.5^{+}}{\lim }(\mathrm{bx}+\mathrm{d})$$$$\frac{1}{4}\mathrm{c}=\frac{1}{2}\mathrm{b}\Rightarrow \mathrm{c}=2\mathrm{b}$$

Commented by M±th+et£s last updated on 06/Apr/20

$$godblessyousir$$$$$$

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