giup to bai nay kho qua

N

ngochuyen94_nd

Xet ham so f(x)=cosx + x^2/2-1
dao ham bac 1 f' =x - sinx
dao ham tiep f"=1-cosx\geq0 voi\forallx
\Rightarrowf' dong bien tren (0;+\infty)
Ma f' lien tuc tren [0;+\infty]
\Rightarrowf' dong bien tren [0;+\infty]\Rightarrow\forallx > 0\Rightarrowf'(x)>f'(0)\Leftrightarrowf'(x)>0
\Rightarrowf(x) dong bien tren (0;+\infty)
ma f(x) lien tuc tren [0;+\infty)
\Rightarrowf(x) dong bien tren [0;+\infty)
voi x>0\Rightarrowf(x)>f(0)\Leftrightarrowcox + x^2/2-1>0(dpcm)
 
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