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Question Number 145318 Answers: 1 Comments: 0

Let f:[0,1]→R be a differentiable function such that f(f(x))=x for all x∈[0,1] and f(0)=1. If n is a positive integer, evaluate the following integral: ∫_0 ^( 1) (x−f(x))^(2n) dx

$Let f : [0, 1] \to R be a differentiable function$ $such that f (f (x)) = x for all x \in [0, 1] and$ $f (0) = 1 .$ $If n is a positive integer, evaluate the$ $following integral :$ $\int_{0}^{1} {(x - f (x))}^{2 n} d x$

Question Number 145316 Answers: 2 Comments: 2

Question Number 145314 Answers: 0 Comments: 2

Let a,b ≥ 0 and (a+1)(b+1) = (a+b)^2 . Prove that (a+b)(√((a+1)^3 +(b+1)^3 )) ≤ (a+1)^2 +(b+1)^2 ≤ (1/2)[(a+1)^3 +(b+1)^3 ]

$Let a, b ⩾ 0 and (a + 1) (b + 1) = {(a + b)}^{2} . Prove that$ $(a + b) \sqrt{{(a + 1)}^{3} + {(b + 1)}^{3}} ⩽ {(a + 1)}^{2} + {(b + 1)}^{2} ⩽ \frac{1}{2} [{(a + 1)}^{3} + {(b + 1)}^{3}]$

Question Number 145309 Answers: 0 Comments: 0

Question Number 145304 Answers: 1 Comments: 0

1+((3x)/(1!)) +((5x^2 )/(2!))+((7x^3 )/(3!))+((9x^4 )/(4!))+...+∞=?

$1 + \frac{3 x}{1!} + \frac{{5 x}^{2}}{2!} + \frac{{7 x}^{3}}{3!} + \frac{{9 x}^{4}}{4!} + . . . + \infty = ?$

Question Number 145305 Answers: 1 Comments: 2

Re^ soudre (((8/(sin^2 (x))) + 1)/((1/(cos^2 (x))) + tan^2 (x))) = cotan^2 (x)+(4/3)

$R \overset{´}{e s o u d r e} \frac{\frac{8}{\sin^{2} (x)} + 1}{\frac{1}{\cos^{2} (x)} + \tan^{2} (x)} = {cotan}^{2} (x) + \frac{4}{3}$

Question Number 145300 Answers: 1 Comments: 0

yy′ = x e^(x/y)

${yy}^{'} = x e^{\frac{x}{y}}$

Question Number 145294 Answers: 2 Comments: 0

Given a polynomial p(x)=x^4 +4x^3 +(2p+2)x^2 +(2p+5q+2)x+3q+2r. If p(x)= (x^3 +2x^2 +8x+6)Q(x) then what the value of (p+2q)r .

$Given a polynomial$ $p (x) = x^{4} + {4 x}^{3} + (2 p + 2) x^{2} + (2 p + 5 q + 2) x + 3 q + 2 r .$ $If p (x) = (x^{3} + {2 x}^{2} + 8 x + 6) Q (x)$ $then what the value of$ $(p + 2 q) r .$

Question Number 145290 Answers: 2 Comments: 0

Question Number 145286 Answers: 3 Comments: 0

Given the function f(x) =((6x^2 −x^3 ))^(1/3) Find the oblique assymptote(s) of the function.

$Given the function$ $f (x) = \sqrt[3]{6 x^{2} - x^{3}}$ $Find the oblique assymptote (s) of the function .$

Question Number 145285 Answers: 0 Comments: 1

x=2−2+2−2+2−…+2−2+2=2

$x = 2 - 2 + 2 - 2 + 2 - \dots + 2 - 2 + 2 = 2$

Question Number 145282 Answers: 1 Comments: 0

Question Number 145280 Answers: 1 Comments: 0

if x^2 =x+2 find ((x^3 +1)/((x+1)^2 )) = ?

$i f x^{2} = x + 2 f i n d \frac{x^{3} + 1}{{(x + 1)}^{2}} = ?$

Question Number 145279 Answers: 1 Comments: 0

2^(a!) + 2^(b!) + 2^(c!) = x Find natural numbers a;b;c such that the number “x” is a cube of any number.

$2^{a!} + 2^{b!} + 2^{c!} = x$ $F i n d n a t u r a l n u m b e r s a; b; c s u c h$ $t h a t t h e n u m b e r ‘ ‘ x^{″} i s a c u b e o f$ $a n y n u m b e r .$

Question Number 145274 Answers: 1 Comments: 0

∫_(∣z∣=1) ((f^− (z))/(z−a))dz

$\int_{∣ z ∣= 1} \frac{\bar{f} (z)}{z - a} d z$

Question Number 145273 Answers: 1 Comments: 0

show that ∀x∈R x−1≤E(x)≤x

$s h o w t h a t \forall x \in R x - 1 ⩽ E (x) ⩽ x$

Question Number 145270 Answers: 1 Comments: 0

# Calculus ( I ) # Σ_(n=1) ^∞ Arccot(3 +((n ( n + 1))/3) )= ? .....

$You can't use 'macro parameter character #' in math mode$ $\underset{n = 1}{\sum^{\infty}} Arccot (3 + \frac{n (n + 1)}{3}) = ?$ $. . . . .$

Question Number 145259 Answers: 1 Comments: 0

∫ (((3(√x)+2)^5 )/( (√x))) dx = ?

$\int \frac{{(3 \sqrt{x} + 2)}^{5}}{\sqrt{x}} d x = ?$

Question Number 145258 Answers: 0 Comments: 0

Question Number 145256 Answers: 1 Comments: 1

x^x^x =((1/2))^(√2) find x

$x^{x^{x}} = {(\frac{1}{2})}^{\sqrt{2}}$ $find x$

Question Number 145250 Answers: 0 Comments: 3

Question Number 145246 Answers: 1 Comments: 0

prove that a triangle inscribed in a circle of radius r having maximum area is an equilateral triangle with side (√3)r.

$prove that a triangle inscribed$ $in a circle of radius r having maximum$ $area is an equilateral triangle with$ $side \sqrt{3} r .$

Question Number 145240 Answers: 1 Comments: 0

Let a,b,c ≥ 0 and a^2 +b^2 +c^2 = 3. Prove that (1) Σ_(cyc) a^3 +Σ_(cyc) (a+b)^3 ≤ 27 (2) a^3 +b^3 +(b+c)^3 +(c+a)^3 ≥ (1/2)[c^3 +(a+b)^3 ] (3) For a≥b≥c≥0, a^3 +b^3 +(b+c)^3 +(c+a)^3 ≤ 2[c^3 +(a+b)^3 ]

$Let a, b, c ⩾ 0 and a^{2} + b^{2} + c^{2} = 3 . Prove that$ $(1) \sum_{c y c} a^{3} + \sum_{c y c} {(a + b)}^{3} ⩽ 27$ $(2) a^{3} + b^{3} + {(b + c)}^{3} + {(c + a)}^{3} ⩾ \frac{1}{2} [c^{3} + {(a + b)}^{3}]$ $(3) For a ⩾ b ⩾ c ⩾ 0,$ $a^{3} + b^{3} + {(b + c)}^{3} + {(c + a)}^{3} ⩽ 2 [c^{3} + {(a + b)}^{3}]$

Question Number 145238 Answers: 2 Comments: 0

Question Number 145231 Answers: 1 Comments: 3

1<a≤b then find ∫_( a) ^( b) tan^(-1) (((3x)/(1-2x^2 )))dx=?

$1 < a ⩽ b t h e n f i n d$ $\underset{a}{\int^{b}} {t a n}^{- 1} (\frac{3 x}{1 - 2 x^{2}}) d x = ?$

Question Number 145229 Answers: 0 Comments: 3

Riddle (clue) 1. I have different types 2. I may be considered natural, whole, positive or negative 3. I am the basic building block of mathematics 4. I am often considered reasonable or rational as well as crazy or irrational 5. I may be terminating or repeating 6. You can locate me on a line bearing my name. who am i?

$Riddle$ $(clue)$ $1 . I have different types$ $2 . I may be considered natural, whole,$ $positive or negative$ $3 . I am the basic building block of$ $mathematics$ $4 . I am often considered reasonable or$ $rational as well as crazy or irrational$ $5 . I may be terminating or repeating$ $6 . You can locate me on a line bearing$ $my name .$ $who am i ?$

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