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Question Number 133589 by benjo_mathlover last updated on 23/Feb/21
For all real number f is given by    f(x)= { ((e^x  + m sin x , if x < 0)),((n(x−1)^2 + x−2 , if x≥0)) :}  what the value m and n is f   differentiable at x = 0 ?
$$\mathrm{For}\:\mathrm{all}\:\mathrm{real}\:\mathrm{number}\:\mathrm{f}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}\: \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{e}^{\mathrm{x}} \:+\:\mathrm{m}\:\mathrm{sin}\:\mathrm{x}\:,\:\mathrm{if}\:\mathrm{x}\:<\:\mathrm{0}}\\{\mathrm{n}\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} +\:\mathrm{x}−\mathrm{2}\:,\:\mathrm{if}\:\mathrm{x}\geqslant\mathrm{0}}\end{cases} \\ $$$$\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{m}\:\mathrm{and}\:\mathrm{n}\:\mathrm{is}\:\mathrm{f}\: \\ $$$$\mathrm{differentiable}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{0}\:? \\ $$
Answered by benjo_mathlover last updated on 23/Feb/21

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