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AllQuestion and Answers: Page 372

Question Number 176684 Answers: 1 Comments: 2

Question Number 176679 Answers: 2 Comments: 0

Eeasy integral.... 𝛀 = ∫_(−∫_0 ^( ∞) e^( −x^( 2) ) dx) ^( ∫_0 ^( ∞) e^( −x^( 2) ) dx) sin^( 2) (t).ln^( 3) ( t + (√(1+t^( 2) )))dt −−−m.n−−−

$E e a s y i n t e g r a l . . . .$ $Ω = \int_{- \int_{0}^{\infty} e^{- x^{2}} d x}^{\int_{0}^{\infty} e^{- x^{2}} d x} {s i n}^{2} (t) . {l n}^{3} (t + \sqrt{1 + t^{2}}) d t$ $- - - m . n - - -$

Question Number 176676 Answers: 3 Comments: 0

If x^3 +(1/x^3 )=1, prove that x^5 +(1/x^5 )=−(x^4 +(1/x^4 ))

$If x^{3} + \frac{1}{x^{3}} = 1,$ $prove that$ $x^{5} + \frac{1}{x^{5}} = - (x^{4} + \frac{1}{x^{4}})$

Question Number 176672 Answers: 1 Comments: 0

Question Number 176673 Answers: 1 Comments: 0

Question Number 176668 Answers: 3 Comments: 0

Question Number 176662 Answers: 3 Comments: 0

sequence V_(n+1) −V_n =n+3^n . Find V_n .

$s e q u e n c e V_{n + 1} - V_{n} = n + 3^{n} . F i n d V_{n} .$

Question Number 176660 Answers: 1 Comments: 1

Question Number 176652 Answers: 1 Comments: 0

f(x,y)= { ((e^(1/(r^2 −1)) if r<1, where r=∥(x,y)∥)),((0 if r≥1)) :} show that f(x,y) is continuous in R^2

$f (x, y) = {\begin{cases} e^{\frac{1}{r^{2} - 1}} if r < 1, where r =∥ (x, y) ∥ \\ 0 if r ⩾ 1 \end{cases}$ $show that f (x, y) is continuous in R^{2}$

Question Number 176648 Answers: 2 Comments: 1

∫ (dx/(a+bcosx)) ∫ (dx/(a−bsinx))

$\int \frac{d x}{a + b c o s x}$ $\int \frac{d x}{a - b s i n x}$

Question Number 176643 Answers: 0 Comments: 2

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=?

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

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