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Question Number 165357 Answers: 1 Comments: 2

Question Number 165355 Answers: 1 Comments: 0

Question Number 165354 Answers: 0 Comments: 0

Question Number 165349 Answers: 1 Comments: 0

Question Number 165339 Answers: 1 Comments: 0

# Advanced Calculus # Let , f : R → Q is a continuous function . prove that ” f ” is a constant function . ■ m.n ∗ Adopted from mathematical analysis book ∗ −−−−−−−−−−−−−−

$You can't use 'macro parameter character #' in math mode$ $L e t, f : R \to Q i s a c o n t i n u o u s$ $f u n c t i o n . p r o v e t h a t^{″} f^{″} i s a$ $c o n s t a n t f u n c t i o n . ◼ m . n$ $* A d o p t e d f r o m m a t h e m a t i c a l a n a l y s i s b o o k *$ $- - - - - - - - - - - - - -$

Question Number 165329 Answers: 2 Comments: 0

prove ( n∈ N ) 3(n+1) ∣ n^( 3) + (n+1)^( 3) + (n+2 )^( 3)

$p r o v e (n \in N)$ $3 (n + 1) ∣ n^{3} + {(n + 1)}^{3} + {(n + 2)}^{3}$

Question Number 165328 Answers: 3 Comments: 0

prove that Nice Integral 𝛗=∫_0 ^( 1) (( tan^( −1) (x^( (3/2)) ))/x^( 2) ) dx =((π + (√3) ln(7 +4(√3) ))/4) ■ m.n −−−−−−−−−

$p r o v e t h a t$ $N i c e I n t e g r a l$ $ϕ = \int_{0}^{1} \frac{{t a n}^{- 1} (x^{\frac{3}{2}})}{x^{2}} d x = \frac{π + \sqrt{3} l n (7 + 4 \sqrt{3})}{4} ◼ m . n$ $- - - - - - - - -$

Question Number 165322 Answers: 1 Comments: 2

who can prove that 2^n −1produces a prime number when n is a prime number

$w h o c a n p r o v e t h a t 2^{n} - 1 p r o d u c e s$ $a p r i m e n u m b e r w h e n n i s a$ $p r i m e n u m b e r$

Question Number 165321 Answers: 2 Comments: 0

Question Number 165320 Answers: 1 Comments: 0

Ω = ∫_0 ^( (π/4)) cos (2x ).e^( ⌊ sin(x)+ cos(x) ⌋) dx ⌊ x ⌋= max { m ∈ Z ∣ m ≤ x } −−−−

$Ω = \int_{0}^{\frac{π}{4}} c o s (2 x) . e^{⌊ s i n (x) + c o s (x) ⌋} d x$ $⌊ x ⌋ = m a x {m \in Z ∣ m ⩽ x}$ $- - - -$

Question Number 165314 Answers: 0 Comments: 2

sin^2 1+sin^2 2+sin^2 3+.....+sin^2 90=?

$\sin^{2} 1 + \sin^{2} 2 + \sin^{2} 3 + . . . . . + {s i n}^{2} 90 = ?$

Question Number 165301 Answers: 1 Comments: 0

Question Number 165296 Answers: 2 Comments: 1

Question Number 165307 Answers: 0 Comments: 0

Question Number 165291 Answers: 1 Comments: 0

Question Number 165309 Answers: 0 Comments: 0

(6/(6+(√6))) + (6/(6^2 +(√6))) +(6/(6^3 +(√6))) +...+(6/(6^(1000) +(√6))) =?

$\frac{6}{6 + \sqrt{6}} + \frac{6}{6^{2} + \sqrt{6}} + \frac{6}{6^{3} + \sqrt{6}} + . . . + \frac{6}{6^{1000} + \sqrt{6}} = ?$

Question Number 165262 Answers: 2 Comments: 0

find the sum Σ_(n=1) ^∞ ((1/2))^n + i ( (1/3) )^n

$f i n d t h e s u m \underset{n = 1}{\sum^{\infty}} {(\frac{1}{2})}^{n} + i {(\frac{1}{3})}^{n}$

Question Number 165255 Answers: 1 Comments: 0

nice integral ∫_0 ^1 (1/x)ln(Σ_(m=0) ^n x^m )dx=? −−−−−−−−−−−−−by MATH.AMIN

$nice integral$ $\int_{0}^{1} \frac{1}{x} \ln (\underset{m = 0}{\sum^{n}} x^{m}) dx = ?$ $- - - - - - - - - - - - - by MATH . AMIN$

Question Number 165243 Answers: 1 Comments: 0

⌊Find the value of x???⌋ ⌊5x + ((5x)/((5 + 5)^5 )) × (−5x) ÷ 555x −55x ×((5÷5)/5) + x = 555555555555555⌋ ^(proof:z.a)

$⌊ Find the value of x ? ? ? ⌋$ $⌊ 5 x + \frac{5 x}{{(5 + 5)}^{5}} \times (- 5 x) \div 555 x - 55 x \times \frac{5 \div 5}{5} + x = 555555555555555 ⌋$ $^{proof : z . a}$

Question Number 165240 Answers: 1 Comments: 0

soit la serie de fonction Σ_(n=2 ) (x^n /(nx+ln(n))) etudie la convergence simple sur [0,1[

$s o i t l a s e r i e d e f o n c t i o n \sum_{n = 2} \frac{x^{n}}{n x + l n (n)}$ $e t u d i e l a c o n v e r g e n c e s i m p l e s u r [0, 1 [$

Question Number 165234 Answers: 0 Comments: 1

Question Number 165253 Answers: 3 Comments: 0

Question Number 165232 Answers: 1 Comments: 1

Question Number 165250 Answers: 0 Comments: 1

Question Number 165229 Answers: 0 Comments: 1

Σ_(i=1) ^(n=∞) lim_(x→0) ((xyn^x )/(nx_1 ))xz∫((xn^n x)/(nx^n y))dn (√(c^n +n_1 )) ∫((xn^(n!) )/(n^n xn^x ))dn

$\underset{i = 1}{\sum^{n = \infty}} \lim_{x \to 0} \frac{{x y n}^{x}}{{n x}_{1}} x z \int \frac{{x n}^{n} x}{{n x}^{n} y} d n$ $\sqrt{c^{n} + n_{1}}$ $\int \frac{{x n}^{n!}}{n^{n} {x n}^{x}} d n$

Question Number 165226 Answers: 1 Comments: 0

make x the subject of the formula; a^x +bx+c=0

$m a k e x t h e s u b j e c t o f t h e f o r m u l a;$ $a^{x} + b x + c = 0$

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