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AllQuestion and Answers: Page 742

Question Number 138891 Answers: 1 Comments: 1

Question Number 138879 Answers: 1 Comments: 0

Question Number 138909 Answers: 3 Comments: 0

∫ ((x^6 −1)/((x^3 −1)^3 )) dx=?

$\int \frac{x^{6} - 1}{{(x^{3} - 1)}^{3}} dx = ?$

Question Number 138872 Answers: 2 Comments: 0

Question Number 138863 Answers: 2 Comments: 0

∣2x−1∣ ≤ (4/( (√(x+2)))) + 1

$∣ 2 x - 1 ∣ ⩽ \frac{4}{\sqrt{x + 2}} + 1$

Question Number 138860 Answers: 1 Comments: 0

Prove:: ∫_0 ^∞ ((x^3 −sin^3 x)/x^5 )dx=((13)/(32))π

$P r o v e :: \int_{0}^{\infty} \frac{x^{3} - \sin^{3} x}{x^{5}} d x = \frac{13}{32} π$

Question Number 138855 Answers: 0 Comments: 0

Question Number 138851 Answers: 3 Comments: 0

Find max value of x^2 −3xy−2y^2 subject to x^2 +xy+y^2 =1.

$F i n d m a x v a l u e o f$ $x^{2} - 3 x y - 2 y^{2} s u b j e c t t o$ $x^{2} + x y + y^{2} = 1 .$

Question Number 138850 Answers: 0 Comments: 0

x^(−log (x)+4) < (1/(16))x

$x^{- \log (x) + 4} < \frac{1}{16} x$

Question Number 138843 Answers: 0 Comments: 0

Question Number 138842 Answers: 0 Comments: 0

Find the sum to infinity 1+((3x)/(1!))+((5x^2 )/(2!))+((7x^3 )/(3!))+..

$F i n d t h e s u m t o i n f i n i t y$ $1 + \frac{3 x}{1!} + \frac{5 x^{2}}{2!} + \frac{7 x^{3}}{3!} + . .$

Question Number 138835 Answers: 0 Comments: 5

x^3 −9x+1=0

$x^{3} - 9 x + 1 = 0$

Question Number 138831 Answers: 1 Comments: 0

Why is the ammeter always connected in series and the voltmeter in parallel?

$W h y i s t h e a m m e t e r a l w a y s c o n n e c t e d i n s e r i e s$ $a n d t h e v o l t m e t e r i n p a r a l l e l ?$

Question Number 138829 Answers: 1 Comments: 0

Question Number 138828 Answers: 1 Comments: 0

Question Number 138827 Answers: 1 Comments: 0

Solve for real numbers: { ((−a^1 −b^2 −c^3 =2024^(12) )),((−a^(−1) −b^(−2) −c^(−3) =2024^(−12) )),((a^1 b^2 c^3 =2024^(24) )) :}

$S o l v e f o r r e a l n u m b e r s :$ ${\begin{cases} - a^{1} - b^{2} - c^{3} = 2024^{12} \\ - a^{- 1} - b^{- 2} - c^{- 3} = 2024^{- 12} \\ a^{1} b^{2} c^{3} = 2024^{24} \end{cases}$

Question Number 138823 Answers: 1 Comments: 0

......Nice ... Calculus...... Evaluate:: 𝛗=Σ_(n=1) ^∞ (1/)=?

$. . . . . . N i c e . . . C a l c u l u s . . . . . .$ $E v a l u a t e :: ϕ = \underset{n = 1}{\sum^{\infty}} \frac{1}{} = ?$

Question Number 138822 Answers: 0 Comments: 0

Question Number 138821 Answers: 3 Comments: 1

....... nice .. .. .. calculus...... find the value of: Θ=Σ_(n=−∞ ) ^∞ (1/(6n^2 +5n+1))=?

$. . . . . . . n i c e . . . . . . c a l c u l u s . . . . . .$ $f i n d t h e v a l u e o f :$ $Θ = \underset{n = - \infty}{\sum^{\infty}} \frac{1}{6 n^{2} + 5 n + 1} = ?$

Question Number 138819 Answers: 5 Comments: 0

(1)::f(x)=∫_0 ^1 ∣x−2t∣dt, ∫_0 ^3 f(x)dx=? −−−−−−−−−−−−−−−−−−− (2)::f(x)=x^2 ∙∫_1 ^x (dt/(t^3 −3t^2 +3t)), f^((2019)) (1)=?

$(1) :: f (x) = \int_{0}^{1} ∣ x - 2 t ∣ d t, \int_{0}^{3} f (x) d x = ?$ $- - - - - - - - - - - - - - - - - - -$ $(2) :: f (x) = x^{2} \cdot \int_{1}^{x} \frac{d t}{t^{3} - 3 t^{2} + 3 t}, f^{(2019)} (1) = ?$

Question Number 138810 Answers: 1 Comments: 0

∫_( 0) ^( π/2) ((xsin(x))/(1−cosx))∙log(1+cosx)dx=?

$\underset{0}{\int^{π / 2}} \frac{x s i n (x)}{1 - c o s x} \cdot l o g (1 + c o s x) d x = ?$

Question Number 138801 Answers: 2 Comments: 0

lim_( n→∞) (∫_0 ^( 1) (((1−x)^n e^x )/(n!))dx)=?

${l i m}_{n \to \infty} (\int_{0}^{1} \frac{{(1 - x)}^{n} e^{x}}{n!} d x) = ?$

Question Number 138799 Answers: 2 Comments: 0

∫_0 ^(π/2) ln(tan(x)−α)dx=... α∈C

$\int_{0}^{\frac{π}{2}} \ln (\tan (x) - α) d x = . . .$ $α \in C$

Question Number 138797 Answers: 2 Comments: 0

Let a,b,c be positive constants. Among all real number x and y satisfying ax+by=c , find the maximum value of product xy.

$L e t a, b, c b e p o s i t i v e c o n s t a n t s .$ $A m o n g a l l r e a l n u m b e r x a n d y$ $s a t i s f y i n g a x + b y = c, f i n d t h e$ $m a x i m u m v a l u e o f p r o d u c t$ $x y .$

Question Number 138789 Answers: 0 Comments: 0

Question Number 138783 Answers: 0 Comments: 4

Solve for real numbees: { ((a^(16) +1=((a+b)/2))),((b^(16) +1=((b+c)/2))),((c^(16) +1=((c+x)/2))) :}

$S o l v e f o r r e a l n u m b e e s :$ ${\begin{cases} a^{16} + 1 = \frac{a + b}{2} \\ b^{16} + 1 = \frac{b + c}{2} \\ c^{16} + 1 = \frac{c + x}{2} \end{cases}$

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