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AllQuestion and Answers: Page 1447

Question Number 60981 Answers: 2 Comments: 6

Question Number 60976 Answers: 0 Comments: 1

find Σ_(n=1) ^∞ (1/n^2 ) by use of integral ∫_0 ^(π/2) ln(2cosθ)dθ .

$f i n d \sum_{n = 1}^{\infty} \frac{1}{n^{2}} b y u s e o f i n t e g r a l \int_{0}^{\frac{π}{2}} l n (2 c o s θ) d θ .$

Question Number 60980 Answers: 1 Comments: 2

Solve for x, y, z x(y + z) = 33 ..... (i) y(z + x) = 35 ..... (ii) z(x + y) = 14 ..... (iii)

$Solve for x, y, z$ $x (y + z) = 33 . . . . . (i)$ $y (z + x) = 35 . . . . . (ii)$ $z (x + y) = 14 . . . . . (iii)$

Question Number 60967 Answers: 0 Comments: 4

study the integral ∫_(−∞) ^(+∞) (1−cos((2/(x^2 +1))))dx

$s t u d y t h e i n t e g r a l \int_{- \infty}^{+ \infty} (1 - c o s (\frac{2}{x^{2} + 1})) d x$

Question Number 60960 Answers: 0 Comments: 2

find ∫_(−∞) ^(+∞) tan((1/(1+x^2 )))dx

$f i n d \int_{- \infty}^{+ \infty} t a n (\frac{1}{1 + x^{2}}) d x$

Question Number 60955 Answers: 1 Comments: 4

Question Number 60948 Answers: 0 Comments: 1

Question Number 60946 Answers: 3 Comments: 4

Find x: x^x = 2x

$Find x : x^{x} = 2 x$

Question Number 60944 Answers: 1 Comments: 1

∫(dx/((1+x^2 )^(3/2) )) solve this pls

$\int \frac{d x}{{(1 + x^{2})}^{\frac{3}{2}}}$ $s o l v e t h i s p l s$

Question Number 60938 Answers: 0 Comments: 1

∫((csc^(2019) (x))/(sec^5 (x))) tan^2 (x) dx

$\int \frac{{c s c}^{2019} (x)}{{s e c}^{5} (x)} {t a n}^{2} (x) d x$

Question Number 60921 Answers: 1 Comments: 0

x^2 (d^2 y/dx^2 ) + x(dy/dx) + y=0 please solve this Euler equation

$x^{2} \frac{d^{2} y}{{d x}^{2}} + x \frac{d y}{d x} + y = 0$ $p l e a s e s o l v e t h i s E u l e r e q u a t i o n$

Question Number 60915 Answers: 0 Comments: 0

Let Fibonacci sequence (F_n ) _(n≥0) where F_0 = 0, F_1 = 1, and F_(n+2) = F_(n+1) + F_n , ∀ n ≥ 0 . Find the least of natural numbers n so that F_n and F_(n+1) − 1 can be divided by F_(2019) .

$L e t F i b o n a c c i s e q u e n c e (F_{n})_{n ⩾ 0}$ $w h e r e F_{0} = 0, F_{1} = 1, a n d F_{n + 2} = F_{n + 1} + F_{n}, \forall n ⩾ 0 .$ $F i n d t h e l e a s t o f n a t u r a l n u m b e r s n s o t h a t$ $F_{n} a n d F_{n + 1} - 1 c a n b e d i v i d e d b y F_{2019} .$

Question Number 60906 Answers: 0 Comments: 1

Question Number 60905 Answers: 3 Comments: 0

if x+(1/x)=(√3).find x^(24) +x^(18) +x^6 +1

$i f x + \frac{1}{x} = \sqrt{3} . f i n d$ $x^{24} + x^{18} + x^{6} + 1$

Question Number 60901 Answers: 1 Comments: 0

find ∫ arctan((1/(1+x^2 )))dx

$f i n d \int a r c t a n (\frac{1}{1 + x^{2}}) d x$

Question Number 60894 Answers: 0 Comments: 0

study the convergence of ∫_0 ^1 (((√(1+2x))−(√(1+x)))/(ln(1+x)))dx and determine its value.

$s t u d y t h e c o n v e r g e n c e o f$ $\int_{0}^{1} \frac{\sqrt{1 + 2 x} - \sqrt{1 + x}}{l n (1 + x)} d x a n d d e t e r m i n e i t s$ $v a l u e .$

Question Number 60893 Answers: 1 Comments: 1

calculate ∫_0 ^(π/2) (dx/((√2)cos^2 x +(√3)sin^2 x))

$c a l c u l a t e \int_{0}^{\frac{π}{2}} \frac{d x}{\sqrt{2} {c o s}^{2} x + \sqrt{3} {s i n}^{2} x}$

Question Number 60910 Answers: 1 Comments: 7

Question Number 60888 Answers: 1 Comments: 1

Question Number 60873 Answers: 2 Comments: 5

Question Number 60881 Answers: 0 Comments: 3

∫_(−π) ^π sin((1/(1−x^2 ))) dx

$\underset{- π}{\int^{π}} s i n (\frac{1}{1 - x^{2}}) d x$

Question Number 60862 Answers: 0 Comments: 0

Question Number 60854 Answers: 2 Comments: 4

(x^4 −3x^2 +2x+1)/(x−1)

$(x^{4} - 3 x^{2} + 2 x + 1) / (x - 1)$

Question Number 60853 Answers: 2 Comments: 0

(√(5−12i))+(√(5+12i))=?

$\sqrt{5 - 12 i} + \sqrt{5 + 12 i} = ?$

Question Number 60849 Answers: 1 Comments: 5

For all θ in [0, π/2] show that cos(sinθ)≥sin(cosθ).

$F o r a l l θ i n [0, π / 2] s h o w t h a t c o s (s i n θ) ⩾ s i n (c o s θ) .$

Question Number 61612 Answers: 0 Comments: 7

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