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Given-f-x-sin2x-2cos2x-find-f-pi-4-hence-given-g-x-x-0-x-2-3x-x-2-2-x-3-for-a-total-range-of-0-x-3-sketch-the-graph-for-y-g-x-and-find-the-area-with-makes-with-the-x-axis




Question Number 49703 by Rio Michael last updated on 09/Dec/18
Given f(x)= sin2x+2cos2x  find f′((π/4))  hence given g(x) =  { ((x,   0≤x≤2)),((3x−x^2 ,  2≤x≤3)) :}  for a total range of 0≤x≤3  sketch the graph for y=g(x)  and find the area with makes with the x−axis  otherwise, find   the composite function  gf  in the range  2≤x≤3.
$${Given}\:{f}\left({x}\right)=\:{sin}\mathrm{2}{x}+\mathrm{2}{cos}\mathrm{2}{x} \\ $$$${find}\:{f}'\left(\frac{\pi}{\mathrm{4}}\right) \\ $$$${hence}\:{given}\:{g}\left({x}\right)\:=\:\begin{cases}{{x},\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}}\\{\mathrm{3}{x}−{x}^{\mathrm{2}} ,\:\:\mathrm{2}\leqslant{x}\leqslant\mathrm{3}}\end{cases} \\ $$$${for}\:{a}\:{total}\:{range}\:{of}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:\:{sketch}\:{the}\:{graph}\:{for}\:{y}={g}\left({x}\right) \\ $$$${and}\:{find}\:{the}\:{area}\:{with}\:{makes}\:{with}\:{the}\:{x}−{axis} \\ $$$${otherwise},\:{find}\:\:\:{the}\:{composite}\:{function}\:\:{gf}\:\:{in}\:{the}\:{range} \\ $$$$\mathrm{2}\leqslant{x}\leqslant\mathrm{3}. \\ $$

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