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Relation and FunctionsQuestion and Answers: Page 1

Question Number 218673 Answers: 3 Comments: 1

Question Number 218311 Answers: 1 Comments: 0

Question Number 218256 Answers: 2 Comments: 0

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Question Number 216077 Answers: 1 Comments: 0

Find the largest value of the non negative integer p for which lim_(x→1) {((− px + sin(x − 1) + p)/(x + sin(x − 1) − 1))}^((1 − x)/(1 − (√x))) = (1/4) .

$Find the largest value of the non negative$ $integer p for which$ $\lim_{x \to 1} {\frac{- p x + \sin (x - 1) + p}{x + \sin (x - 1) - 1}}^{\frac{1 - x}{1 - \sqrt{x}}} = \frac{1}{4} .$

Question Number 215887 Answers: 0 Comments: 2

Question Number 215331 Answers: 1 Comments: 0

Question Number 214644 Answers: 1 Comments: 0

((−6)/7)/((−7)/6)

$\frac{- 6}{7} / \frac{- 7}{6}$

Question Number 213291 Answers: 1 Comments: 0

Find domain of y_(213291) : y_(213291) =((3+e^((x^2 −3x+2)/(x−6)) )/(log_(3/4) (√(x^2 −(1/4)))))

$F i n d d o m a i n o f y_{213291} :$ $y_{213291} = \frac{3 + e^{\frac{x^{2} - 3 x + 2}{x - 6}}}{\log_{\frac{3}{4}} \sqrt{x^{2} - \frac{1}{4}}}$

Question Number 212518 Answers: 2 Comments: 0

⇃

$\underset{⏟}{⇃} \underset{―}{}$

Question Number 209707 Answers: 0 Comments: 0

a,b ∈C : ab^− + b = 0 f : z′ = az^− + b such that f(M) = M′ 1. let z_A = z and z_(A′) = z′ and f(A) = A show that 2Re(b^− z) = bb^− (A is the set of invariant points and describes a line (△) ) 2. Deduce that (△) is a line with gradient u^( →) with affix z_u^→ = ib 3. show that (z_(MM ′) /z_u ) = ((bb^− − 2Re(bz^− ))/(ibb^− )) 4. show that 2Re(b^− z_0 ) = bb^_ where z_0 = ((z + z ′)/2) 5. Deduce that for M ∉ (△) , M is a perpendicular bisector of [MM ′]

$a, b \in C : a \bar{b} + b = 0 f : z^{'} = a \bar{z} + b$ $s u c h t h a t f (M) = M^{'}$ $1 . l e t z_{A} = z a n d z_{A^{'}} = z^{'} a n d f (A) = A$ $s h o w t h a t 2 R e (\bar{b z}) = b \bar{b}$ $(A i s t h e s e t o f i n v a r i a n t p o i n t s a n d$ $d e s c r i b e s a l i n e (△))$ $2 . D e d u c e t h a t (△) i s a l i n e w i t h$ $g r a d i e n t \vec{u} w i t h a f f i x z_{\vec{u}} = i b$ $3 . s h o w t h a t \frac{z_{M M^{'}}}{z_{u}} = \frac{b \bar{b} - 2 R e (b \bar{z})}{i b \bar{b}}$ $4 . s h o w t h a t 2 R e ({\bar{b z}}_{0}) = b \overline{b} w h e r e$ $z_{0} = \frac{z + z^{'}}{2}$ $5 . D e d u c e t h a t f o r M \notin (△), M i s$ $a p e r p e n d i c u l a r b i s e c t o r o f [M M^{'}]$

Question Number 208533 Answers: 2 Comments: 0

z′ = (1/2)(z+(1/z)) z and z′ are complex numbers show that z = 2e^(iθ) show that M′ describes a conic section

$z^{'} = \frac{1}{2} (z + \frac{1}{z})$ $z a n d z^{'} a r e c o m p l e x n u m b e r s$ $s h o w t h a t z = 2 e^{i θ}$ $s h o w t h a t M^{'} d e s c r i b e s a c o n i c s e c t i o n$

Question Number 208431 Answers: 2 Comments: 0

h_a (x) = e^(−x) + ax^2 show that h_a admits a minimum in R

$h_{a} (x) = e^{- x} + {a x}^{2}$ $s h o w t h a t h_{a} a d m i t s a m i n i m u m i n R$

Question Number 208418 Answers: 1 Comments: 0

u_(n+1) = u_n −u_n ^3 ; u_0 ∈ ]0, 1[ . show that u_n ∈ ]0, 1[ . show that u_n converges to 0 v_n = (1/u_(n+1) ^2 ) − (1/u_n ^2 ) . express v_n interms of u_n . show that v_n converges to 2 f(x) = ((2−x)/((1−x)^2 )) . show that f is increasing and deduce that v_n is decreasing . show that v_n ≥ 2

$u_{n + 1} = u_{n} - u_{n}^{3}; u_{0} \in] 0, 1 [$ $. s h o w t h a t u_{n} \in] 0, 1 [$ $. s h o w t h a t u_{n} c o n v e r g e s t o 0$ $v_{n} = \frac{1}{u_{n + 1}^{2}} - \frac{1}{u_{n}^{2}}$ $. e x p r e s s v_{n} i n t e r m s o f u_{n}$ $. s h o w t h a t v_{n} c o n v e r g e s t o 2$ $f (x) = \frac{2 - x}{{(1 - x)}^{2}}$ $. s h o w t h a t f i s i n c r e a s i n g a n d d e d u c e t h a t$ $v_{n} i s d e c r e a s i n g$ $. s h o w t h a t v_{n} ⩾ 2$

Question Number 208103 Answers: 1 Comments: 0

Find inf{(m/n) ∣ m, n ∈ N, m<n−2}

$Find \inf {\frac{m}{n} ∣ m, n \in N, m < n - 2}$

Question Number 207390 Answers: 0 Comments: 1

Question Number 207314 Answers: 1 Comments: 0

let f:R→R be a continuous function then show that (1) if f(x) = f(x^2 ) ∀ x ∈R then f is a constant function (2) if f(x) = f(2x+1) ∀x∈R then f is a constant function

$let f : R \to R be a continuous function then$ $show that$ $(1) if f (x) = f (x^{2}) \forall x \in R then f is a constant$ $function$ $(2) if f (x) = f (2 x + 1) \forall x \in R then f is a$ $constant function$

Question Number 207085 Answers: 2 Comments: 0

Let f be a function with the following properties: (i) f(1) =1 (ii) f(2n)=n.f(n) for any positive integer n. Find the value of f(2^(10) ) a)1 b) 2^(10 ) c) 2^(35) d) 2^(45)

$L e t f b e a f u n c t i o n w i t h t h e f o l l o w i n g$ $p r o p e r t i e s : (i) f (1) = 1 (i i) f (2 n) = n . f (n) f o r$ $a n y p o s i t i v e i n t e g e r n . F i n d t h e v a l u e$ $o f f (2^{10})$ $a) 1 b) 2^{10} c) 2^{35} d) 2^{45}$

Question Number 206993 Answers: 1 Comments: 0

If the nth term of a sequence is given by ((n^2 −2n)/4) ,what is the sum of n terms of the sequence?

$I f t h e n t h t e r m o f a s e q u e n c e i s$ $g i v e n b y \frac{n^{2} - 2 n}{4}, w h a t i s t h e s u m o f n$ $t e r m s o f t h e s e q u e n c e ?$

Question Number 206442 Answers: 1 Comments: 0

Question Number 206151 Answers: 1 Comments: 0

Question Number 206136 Answers: 1 Comments: 0

Question Number 205919 Answers: 1 Comments: 0

write the following recursive function in explicit form f(1)=1 f(n+1)=(n+1)f(n)+n!

$write the following recursive function in explicit form$ $f (1) = 1$ $f (n + 1) = (n + 1) f (n) + n!$

Question Number 205262 Answers: 1 Comments: 0

nature of the serie Σ_(n≥1) ((ln(n))/n)

$n a t u r e o f t h e s e r i e \sum_{n ⩾ 1} \frac{l n (n)}{n}$

Question Number 204478 Answers: 1 Comments: 0

soit f: R^3 →R^3 f(x,y,z)=(x+y,2x−y,x+z) •1 Ecrire la matrice M de cette application dans la base canonique B de R^3 •2 Calculer f(1,2,3)de 2 manieres differentes −en utilisant la definition de f −en utilisant la matrice M •3 determiner bsse de Ker( f) et de Im(f) •4 soient v_1 =(1,1,0) v_2 =(1,2,1) v_3 =(1,3,1) Montrer que la famille E=(v_1 , v_2 , v_3 )est une base de R^3 •5Calculer f(v_1 ) donner ses coordonnes(locus) dans bass E avec f(v_2 )=v_1 +6v_2 −4v_3 f(v_3 )=2v_1 +8v_2 −6v_3 •6 Ecrire la matrice N de f dans base F •7 Retrouver cette matrice a partir de M en utilisant la formule de changement de base

$soit f : R^{3} \to R^{3} f (x, y, z) = (x + y, 2 x - y, x + z)$ $∙ 1 Ecrire la matrice M de cette application$ $dans la base canonique B de R^{3}$ $∙ 2 Calculer f (1, 2, 3) de 2 manieres differentes$ $- en utilisant la definition de f$ $- en utilisant la matrice M$ $∙ 3 determiner bsse de Ker (f) et de I m (f)$ $∙ 4 soient v_{1} = (1, 1, 0) v_{2} = (1, 2, 1) v_{3} = (1, 3, 1)$ $Montrer que la famille E = (v_{1}, v_{2}, v_{3}) est$ $une base de R^{3}$ $∙ 5 Calculer f (v_{1}) donner ses coordonnes (locus)$ $dans bass E$ $avec f (v_{2}) = v_{1} + {6 v}_{2} - {4 v}_{3}$ $f (v_{3}) = {2 v}_{1} + {8 v}_{2} - {6 v}_{3}$ $∙ 6 Ecrire la matrice N de f dans base F$ $∙ 7 Retrouver cette matrice a partir de M$ $en utilisant la formule de changement de base$

Question Number 204426 Answers: 1 Comments: 0

let a , b >0 find all differentiable function f:(0,∞)→(0,∞) such that f′((a/x)) = ((bx)/(f(x))) , ∀ x>0

$let a, b > 0 find all differentiable function$ $f : (0, \infty) \to (0, \infty) such that$ $f^{'} (\frac{a}{x}) = \frac{bx}{f (x)}, \forall x > 0$

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

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