Solve Question 73 step by step

Solve Question 73 step by step 72. tho Let r (x) 2sin2 X —1 lei 2 cos x + sin x then (A) tan* + c Where c is the constant Of (B) excotx + c 73. 74. Let if x if x O Then which of the following can best graph 0.1 (A) (B) x If In = cotnx dx, then 10+11+2(12+13+.. .... equals to: (where u = cotx) 9 u 2

fx=e-1x2, if x00       ,if x=0for x0fx=e-1x2f'x=d dxe-1x2=e-1x2d dx-1x2=e-1x2d dx-x-2=e-1x2--2x-2-1=2x-3e-1x2Note: For x>0, f'x>0 and for x<0, f'x<0f'x=2x-3e-1x2f''x=2x-3d dxe-1x2+2e-1x2d dxx-3f''x=2x-3e-1x22x-3-6e-1x2x-4f''x=2x-32x-3-3x-1f''x=2x-32x3-3xf''x=2x-32-3x2x3f''x=2x-62-3x2Note: if 2-3x2<0 then f''x<0 and if 2-3x2>0 then f''x2-3x2>03x2<2x2<23x2-232<0x-23x+23<0x-23x--23<0Solution of equation x-ax-b<0, where a<b, is given by a<x<b -23<x<23But note 0 is not in domain-23<x<23 and x0Therefore between -23 and 23 f''x>0, so in this interval the graph should be concave upward and rest everywhere it will be concave downwards.Option c looks like the same

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