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Question Number 176638 Answers: 1 Comments: 0

lim_(x→0) ((sin^2 (x)−sin (x^2 ))/(x^2 (cos^2 (x)−cos (x^2 ))))=?

$\lim_{x \to 0} \frac{\sin^{2} (x) - \sin (x^{2})}{x^{2} (\cos^{2} (x) - \cos (x^{2}))} = ?$

Question Number 176637 Answers: 0 Comments: 0

Question Number 176636 Answers: 2 Comments: 2

{ ((p^3 +q^3 =r^2 )),((p^3 +r^3 =q^2 )),((q^3 +r^3 =p^2 )) :} ⇒20pqr =?

${\begin{cases} p^{3} + q^{3} = r^{2} \\ p^{3} + r^{3} = q^{2} \\ q^{3} + r^{3} = p^{2} \end{cases}$ $\Rightarrow 20 p q r = ?$

Question Number 176610 Answers: 1 Comments: 0

Question Number 176607 Answers: 1 Comments: 0

Question Number 176603 Answers: 2 Comments: 6

look the anser

$l o o k t h e a n s e r$

Question Number 176595 Answers: 2 Comments: 0

Question Number 176594 Answers: 0 Comments: 1

𝛗=∫_0 ^( 1) (( ( tanh^( −1) (x))^2 )/((1+x )^( 2) )) dx = ? ≺ solution ≻ note : tanh^( −1) (x)=− (1/2) ln(((1−x)/(1+x))) 𝛗= (1/4)∫_0 ^( 1) (( ln^( 2) (((1−x)/(1+x)) ))/((1+x )^( 2) )) dx =^(((1−x)/(1+x)) = t) (1/8)∫_0 ^( 1) ln^( 2) (t )dt =(1/8_ ) { [t.ln^( 2) (t)]_0 ^( 1) −2∫_0 ^( 1) ln(t)dt} =− (1/4) ∫_0 ^( 1) ln(t)dt= (1/4) ◂ m.n ▶

$ϕ = \int_{0}^{1} \frac{{({t a n h}^{- 1} (x))}^{2}}{{(1 + x)}^{2}} d x = ?$ $≺ s o l u t i o n ≻$ $n o t e : {t a n h}^{- 1} (x) = - \frac{1}{2} l n (\frac{1 - x}{1 + x})$ $ϕ = \frac{1}{4} \int_{0}^{1} \frac{{l n}^{2} (\frac{1 - x}{1 + x})}{{(1 + x)}^{2}} d x$ $\overset{\frac{1 - x}{1 + x} = t}{=} \frac{1}{8} \int_{0}^{1} {l n}^{2} (t) d t$ $= \frac{1}{8_{}} {{[t . {l n}^{2} (t)]}_{0}^{1} - 2 \int_{0}^{1} l n (t) d t}$ $= - \frac{1}{4} \int_{0}^{1} l n (t) d t = \frac{1}{4} ◂ m . n ▸$

Question Number 176592 Answers: 2 Comments: 0

Solve the equation: 2^x + 3^x − 4^x + 6^x − 9^x = 1

$Solve the equation :$ $2^{x} + 3^{x} - 4^{x} + 6^{x} - 9^{x} = 1$

Question Number 176589 Answers: 1 Comments: 0

Question Number 176598 Answers: 1 Comments: 0

x^3 +(1/x^3 )=1 (((x^5 +(1/x^5 ))^3 −1)/(x^5 +(1/x^5 )))=? Q#176387 reposted for a new answer.

$x^{3} + \frac{1}{x^{3}} = 1$ $\frac{{(x^{5} + \frac{1}{x^{5}})}^{3} - 1}{x^{5} + \frac{1}{x^{5}}} = ?$ $You can't use 'macro parameter character #' in math mode$

Question Number 176581 Answers: 1 Comments: 0

Given { ((sin a+sin b=((√2)/2))),((cos a+cos b=((√6)/2))) :} for a,b real numbers. Evaluate sin (a+b). (A)((√3)/2) (D) −((√3)/2) (B) (2/( (√3))) (E)−(2/( (√3))) (C) ((√3)/4)

$Given {\begin{cases} \sin a + \sin b = \frac{\sqrt{2}}{2} \\ \cos a + \cos b = \frac{\sqrt{6}}{2} \end{cases}$ $for a, b real numbers . Evaluate$ $\sin (a + b) .$ $(A) \frac{\sqrt{3}}{2} (D) - \frac{\sqrt{3}}{2}$ $(B) \frac{2}{\sqrt{3}} (E) - \frac{2}{\sqrt{3}}$ $(C) \frac{\sqrt{3}}{4}$

Question Number 176580 Answers: 1 Comments: 0

4^(x^2 −2x+2) −2^(x^2 −2x+3) +2=2^(x^2 −2x+2) x=?

$4^{x^{2} - 2 x + 2} - 2^{x^{2} - 2 x + 3} + 2 = 2^{x^{2} - 2 x + 2}$ $x = ?$

Question Number 176571 Answers: 1 Comments: 0

lim_(x→1) ((lnx)/(1+lnx−1))=?

$\lim_{x \to 1} \frac{l n x}{1 + l n x - 1} = ?$

Question Number 176570 Answers: 2 Comments: 0

(1) ∫^(π/2) _(π/3) ((1+sinx)/(cosx)) dx=?

$(1) {\int_{\frac{π}{3}}}^{\frac{π}{2}} \frac{1 + s i n x}{c o s x} d x = ?$

Question Number 176566 Answers: 0 Comments: 0

−−−− calculate: Φ = Σ_(n=0) ^( ∞) (( 1)/((2n+1 ).e^( 4n+2) )) = ? where ” e ” is euler number. ≺ solution ≻ Φ = Σ_(n=0) ^∞ (1/e^( 4n+2) ) ∫_0 ^( 1) x^( 2n) dx = (1/e^( 2) ) ∫_0 ^( 1) Σ_(n=0) ^∞ ((( x^2 )/e^( 4) ) )^( n) dx = (1/e^( 2) ) ∫_0 ^( 1) (( 1)/(1− ((x/e^( 2) ) )^( 2) )) dx=(1/(2e^( 2) )) ∫_0 ^( 1) (1/(1−(x/e^( 2) ))) +(1/(1+(x/e^( 2) )))dx = (1/2) ln ( ((1+(1/e^( 2) ))/(1−(1/e^( 2) ))) ) = tanh^( −1) ((( 1)/e^( 2) ) ) ∴ Φ = coth^( −1) ( e^( 2) ) ■ m.n

$- - - -$ $c a l c u l a t e : Φ = \underset{n = 0}{\sum^{\infty}} \frac{1}{(2 n + 1) . e^{4 n + 2}} = ?$ $w h e r e^{″} e^{″} i s e u l e r n u m b e r .$ $≺ s o l u t i o n ≻$ $Φ = \underset{n = 0}{\sum^{\infty}} \frac{1}{e^{4 n + 2}} \int_{0}^{1} x^{2 n} d x$ $= \frac{1}{e^{2}} \int_{0}^{1} \underset{n = 0}{\sum^{\infty}} {(\frac{x^{2}}{e^{4}})}^{n} d x$ $= \frac{1}{e^{2}} \int_{0}^{1} \frac{1}{1 - {(\frac{x}{e^{2}})}^{2}} d x = \frac{1}{2 e^{2}} \int_{0}^{1} \frac{1}{1 - \frac{x}{e^{2}}} + \frac{1}{1 + \frac{x}{e^{2}}} d x$ $= \frac{1}{2} l n (\frac{1 + \frac{1}{e^{2}}}{1 - \frac{1}{e^{2}}}) = {t a n h}^{- 1} (\frac{1}{e^{2}})$ $∴ Φ = {c o t h}^{- 1} (e^{2}) ◼ m . n$

Question Number 176565 Answers: 0 Comments: 0

Question Number 176564 Answers: 0 Comments: 0

Question Number 176563 Answers: 1 Comments: 0

is there an iOS version for this app? please

$is there an iOS version for this app ? please$

Question Number 176555 Answers: 1 Comments: 2

ABCD−convex quadrilateral M∈Int(ABCD) , F−area , s−semiperimetr a , b , c−sides. Prove that: ((MA^4 )/b) + ((MB^4 )/c^4 ) + ((MC^4 )/d) + ((MD^4 )/a) ≥ ((2F^2 )/s)

$ABCD - convex quadrilateral$ $M \in Int (ABCD), F - area, s - semiperimetr$ $a, b, c - sides . Prove that :$ $\frac{{MA}^{4}}{b} + \frac{{MB}^{4}}{c^{4}} + \frac{{MC}^{4}}{d} + \frac{{MD}^{4}}{a} ⩾ \frac{{2 F}^{2}}{s}$

Question Number 176554 Answers: 2 Comments: 0

x + (1/x) =ϕ (Golden ratio) then x^( 2000) +(( 1)/x^( 2000) ) = ?

$x + \frac{1}{x} = φ (G o l d e n r a t i o)$ $t h e n$ $x^{2000} + \frac{1}{x^{2000}} = ?$

Question Number 176576 Answers: 0 Comments: 0

Question Number 176549 Answers: 1 Comments: 0

donner la forme trigonometrique de 1/4(cosΠ/9+isinΠ/9)

$d o n n e r l a f o r m e t r i g o n o m e t r i q u e d e 1 / 4 (c o s Π / 9 + i s i n Π / 9)$

Question Number 176547 Answers: 0 Comments: 0

Question Number 176546 Answers: 0 Comments: 0

Question Number 176542 Answers: 1 Comments: 0

Ω = ∫_0 ^( 1) (( x.tanh^( −1) (x))/((1+x)^( 2) ))dx= (1/(24)) (π^( 2) −6)

$Ω = \int_{0}^{1} \frac{x . {t a n h}^{- 1} (x)}{{(1 + x)}^{2}} d x = \frac{1}{24} (π^{2} - 6)$

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