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AllQuestion and Answers: Page 261

Question Number 189941 Answers: 2 Comments: 0

Question Number 189940 Answers: 0 Comments: 0

Question Number 189937 Answers: 0 Comments: 0

Question Number 189932 Answers: 0 Comments: 0

Question Number 189925 Answers: 2 Comments: 1

Question Number 189923 Answers: 1 Comments: 0

∫(dx/(a + btanx))

$\int \frac{d x}{a + b t a n x}$

Question Number 189921 Answers: 2 Comments: 2

Question Number 189919 Answers: 1 Comments: 0

If x,y are real numbers satisfy ((x+40)/y)+((569)/(xy))=((26−y)/x) , then xy=?

$I f x, y a r e r e a l n u m b e r s s a t i s f y$ $\frac{x + 40}{y} + \frac{569}{x y} = \frac{26 - y}{x}, t h e n x y = ?$

Question Number 189958 Answers: 0 Comments: 0

solve y′′′−y′′−y=sect (−(π/2)<x<(π/2))

$solve y^{‴} - y^{″} - y = s e c t (- \frac{π}{2} < x < \frac{π}{2})$

Question Number 189955 Answers: 1 Comments: 0

Question Number 189916 Answers: 2 Comments: 0

when sinx×cosx=−(1/4) find sinx+cosx=?

$when sinx \times cosx = - \frac{1}{4}$ $find sinx + cosx = ?$

Question Number 189901 Answers: 2 Comments: 0

Question Number 189899 Answers: 1 Comments: 0

Question Number 189898 Answers: 1 Comments: 0

Question Number 189897 Answers: 1 Comments: 0

Question Number 189896 Answers: 1 Comments: 0

Question Number 189895 Answers: 1 Comments: 0

Question Number 189894 Answers: 1 Comments: 0

Question Number 189891 Answers: 2 Comments: 1

Question Number 189890 Answers: 0 Comments: 0

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))

$e^{x} > 1 + x (\forall x > 0)$ $s e t : x = \sqrt{\frac{π}{e}} - 1$ $e^{\frac{\sqrt{π}}{\sqrt{e}} - 1} > \frac{\sqrt{π}}{\sqrt{e}} \Rightarrow e^{\frac{\sqrt{π}}{\sqrt{e}}} > \sqrt{π}$ ${(e^{\frac{\sqrt{π}}{\sqrt{e}}})}^{\sqrt{e}} > \sqrt{π}^{\sqrt{e}} \Rightarrow e^{\sqrt{π}} > \sqrt{π}^{\sqrt{e}}$

Question Number 189874 Answers: 2 Comments: 0

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

$\int_{0}^{2} \frac{s i n (x)}{s i n (x) + c o s (x)} d x = ?$

Question Number 189873 Answers: 1 Comments: 0

∫_0 ^( 2) ((x−1)/(x^2 +x+1))dx= ?

$\int_{0}^{2} \frac{x - 1}{x^{2} + x + 1} d x = ?$

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

$A f a r m e r a n d h i s s o n u s e d 20 d a y s$ $t o w e e d a p l o t o f l a n d . I f t h e f a r m e r$ $u s e s 36 d a y s t o w e e d t h e s a m e p l o t o f$ $l a n d, h o w m a n y d a y s w i l l t h e s o n$ $u s e t o w e e d t h e s a m e p l o t o f l a n d$

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

$h o w d o i p r o v e t h i s u s i n g ϵ a n d δ$ $p l e a s e h e l p$ $\lim_{x, y \to (2, 1)} x^{2} y = 4$

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

$i k n o w b_{n} = 0, b u t a_{0} = \frac{4}{3} F_{0} (a c c o r d i n g$ $t o s o l u t i o n) m y a n s w e r i s a_{0} = \frac{8}{3} F_{0}$ $w h e r e d i d i d i d w r o n g h o w t o$ $f i n d a n s w e r (F o u r i e r t r a n s f o r m a t i o n)$ $l i k e p i c t u r e b e l o w (i n t h e c o m m e n t ?$ $f (t) = {\begin{cases} \frac{3 F_{0}}{t_{0}} t, 0 ⩽ t ⩽ \frac{t_{0}}{3} \\ F_{0}, \frac{t_{0}}{3} ⩽ t ⩽ \frac{2 t_{0}}{3} \\ \frac{- 3 F_{0}}{t_{0}} t + 3 F_{0}, \frac{2 t_{0}}{3} ⩽ t ⩽ t_{0} \end{cases}$ $a_{n} = \frac{2}{t_{0}} \int_{0}^{t_{0}} f (t) c o s (n ω t) d t$ $a_{n} = \frac{2}{t_{0}} \int_{0}^{t_{0}} f (t) c o s (n ω t) d t$ $a_{0} = \frac{2}{t_{0}} \int_{0}^{t_{0}} f (t) d t$ $\int_{0}^{\frac{4 t_{0}}{3}} f (t) d t = \int_{0}^{\frac{t_{0}}{3}} \frac{3 F_{0}}{t_{0}} t d t + \int_{\frac{t_{0}}{3}}^{\frac{2 t_{0}}{3}} F_{0} d t + \int_{\frac{2 t_{0}}{3}}^{t_{0}} \frac{- 3 F_{0}}{t_{0}} t + 3 F_{0} d t$ $= {[\frac{3 F_{0}}{t_{0}} t]}_{0}^{\frac{t_{0}}{3}} + {[F_{0} t]}_{\frac{t_{0}}{3}}^{\frac{2 t_{0}}{3}} + {[\frac{- 3 F_{0}}{t_{0}} t + 3 F_{0} t]}_{\frac{2 t_{0}}{3}}^{t_{0}}$ $= F_{0} + \frac{1}{3} F_{0} t_{0} - F_{0} + F_{0} t_{0}$ $= \frac{4}{3} F_{0} t_{0}$ $s o a_{0} = \frac{2}{t_{0}} \times \frac{4}{3} F_{0} t_{0} = \frac{8}{3} F_{0}$

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