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Question Number 189901 Answers: 2 Comments: 0

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Question Number 189896 Answers: 1 Comments: 0

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Question Number 189886 Answers: 0 Comments: 0

e^( x) > 1+ x (∀ x >0 ) set: x=(√(π/e)) −1 e^( ((√π)/( (√e))) −1) > ((√π)/( (√e))) ⇒ e^( ((√π)/( (√e)))) > (√π) ( e^( ((√π)/( (√e)))) )^( (√e)) > (√π)^( (√e)) ⇒ e^( (√π)) > (√(π ))^( (√e))

$$ \\ $$$$\:\:{e}^{\:{x}} \:>\:\mathrm{1}+\:{x}\:\:\:\:\left(\forall\:{x}\:>\mathrm{0}\:\right) \\ $$$$\:\:\:{set}:\:{x}=\sqrt{\frac{\pi}{{e}}}\:−\mathrm{1} \\ $$$$\:\:\:\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:−\mathrm{1}} >\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}\:\Rightarrow\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \:>\:\sqrt{\pi}\: \\ $$$$\:\:\:\:\:\:\left(\:{e}^{\:\frac{\sqrt{\pi}}{\:\sqrt{{e}}}} \right)^{\:\sqrt{{e}}} >\:\sqrt{\pi}\:^{\:\sqrt{{e}}} \:\Rightarrow\:{e}^{\:\sqrt{\pi}} \:>\:\sqrt{\pi\:}\:^{\:\sqrt{{e}}} \\ $$$$ \\ $$

Question Number 189874 Answers: 2 Comments: 0

∫_0 ^( 2) ((sin(x))/(sin(x)+cos(x)))dx= ?

$$\int_{\mathrm{0}} ^{\:\mathrm{2}} \:\:\:\frac{{sin}\left({x}\right)}{{sin}\left({x}\right)+{cos}\left({x}\right)}{dx}=\:? \\ $$

Question Number 189873 Answers: 1 Comments: 0

∫_0 ^( 2) ((x−1)/(x^2 +x+1))dx= ?

$$\int_{\mathrm{0}} ^{\:\mathrm{2}} \frac{{x}−\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}{dx}=\:? \\ $$

Question Number 189872 Answers: 1 Comments: 0

A farmer and his son used 20 days to weed a plot of land . If the farmer uses 36 days to weed the same plot of land , how many days will the son use to weed the same plot of land

$${A}\:{farmer}\:{and}\:{his}\:{son}\:{used}\:\mathrm{20}\:{days}\: \\ $$$${to}\:{weed}\:{a}\:{plot}\:{of}\:{land}\:.\:{If}\:{the}\:{farmer} \\ $$$${uses}\:\mathrm{36}\:{days}\:{to}\:{weed}\:{the}\:{same}\:{plot}\:{of} \\ $$$${land}\:,\:{how}\:{many}\:{days}\:{will}\:{the}\:{son}\: \\ $$$${use}\:{to}\:{weed}\:{the}\:{same}\:{plot}\:{of}\:{land} \\ $$

Question Number 189870 Answers: 1 Comments: 0

how do i prove this using ε and δ please help lim_(x,y→(2,1)) x^2 y=4

$$ \\ $$$$\:{how}\:{do}\:{i}\:{prove}\:{this}\:{using}\:\epsilon\:{and}\:\delta \\ $$$$\:{please}\:{help} \\ $$$$\underset{{x},{y}\rightarrow\left(\mathrm{2},\mathrm{1}\right)} {\mathrm{lim}}\:{x}^{\mathrm{2}} {y}=\mathrm{4} \\ $$$$ \\ $$

Question Number 189865 Answers: 0 Comments: 2

i know b_n =0, but a_0 =(4/3)F_0 (according to solution) my answer is a_0 =(8/3)F_0 where did i did wrong how to find answer (Fourier transformation) like picture below (in the comment? f(t)= { ((((3F_0 )/t_0 )t,0≤t≤(t_0 /3))),((F_0 , (t_0 /3)≤t≤((2t_0 )/3))),((((-3F_0 )/t_0 )t+3F_0 ,((2t_0 )/3)≤t≤t_0 )) :} a_n =(2/t_0 )∫_0 ^t_0 f(t) cos(nωt)dt a_n =(2/t_0 )∫_0 ^t_0 f(t) cos(nωt)dt a_0 =(2/t_0 )∫_0 ^t_0 f(t) dt ∫_0 ^((4t_0 )/3) f(t) dt =∫_0 ^(t_0 /3) ((3F_0 )/t_0 )tdt+∫_(t_0 /3) ^((2t_0 )/3) F_0 dt+∫_((2t_0 )/3) ^t_0 ((-3F_0 )/t_0 )t+3F_0 dt =[((3F_0 )/t_0 )t]_0 ^(t_0 /3) +[F_0 t]_(t_0 /3) ^((2t_0 )/3) +[((-3F_0 )/t_0 )t+3F_0 t]_((2t_0 )/3) ^t_0 =F_0 +(1/3)F_0 t_0 −F_0 +F_0 t_0 =(4/3) F_0 t_0 so a_0 =(2/t_0 )×(4/3)F_0 t_0 =(8/3)F_0

Question Number 189864 Answers: 1 Comments: 0