1
ans
1
cmts
Find the equation of the circle which touches
the circles xΒ² + yΒ² - 2x + 4y = 1, xΒ² + yΒ² - 12x + 2y = 4
and xΒ² + yΒ² + 2x - 12y + 12 = 0.
1
ans
0
cmts
Prove that βnβ₯2
e^(2nβ1) β1 β₯ 2n(2nβ1)
1
ans
2
cmts
Question 223055
7
ans
0
cmts
Question 221413
0
ans
1
cmts
f(x)= (x/(β£ x β£ + 1))
f(f(f(f(x)))) =?
1
ans
1
cmts
f(x)= (1/2^x ) + (1/3^x ) + (1/4^x ) + ... +(1/(4000^x ))
f(2) + f(3) + f(4)+ ... =?
1
ans
1
cmts
Find the maximum value of x^2 y^3 z^4 subject to the condition x+y+z=18
2
ans
0
cmts
Question 219733
1
ans
0
cmts
If ((fog)^(β1) of)(x)= 3xβ8
find g(5).
2
ans
0
cmts
Prove that the sequence a_n =(1/( ((n!))^(1/n) )) is decreasing.
3
ans
1
cmts
Question 218673
1
ans
0
cmts
Question 218311
2
ans
0
cmts
Question 218256
0
ans
2
cmts
Question 217725
1
ans
0
cmts
Find the largest value of the non negative
integer p for which
lim_(xβ1) {((β px + sin(x β 1) + p)/(x + sin(x β 1) β 1))}^((1 β x)/(1 β (βx))) = (1/4) .
0
ans
2
cmts
Question 215887
1
ans
0
cmts
Question 215331
1
ans
0
cmts
((β6)/7)/((β7)/6)
1
ans
0
cmts
Find domain of y_(213291) :
y_(213291) =((3+e^((x^2 β3x+2)/(xβ6)) )/(log_(3/4) (β(x^2 β(1/4)))))
2
ans
0
cmts
f(x)= x^2 β2ax+a(a+1) and
f : [ a, β)β [a, β) .
f(x)= f^(β1) (x)
0
ans
0
cmts
a,b βC : ab^β + b = 0 f : zβ² = az^β + b
such that f(M) = Mβ²
1. let z_A = z and z_(Aβ²) = zβ² and f(A) = A
show that 2Re(b^β z) = bb^β
(A is the set of invariant points and
describes a line (β³) )
2. Deduce that (β³) is a line with
gradient u^( β) with affix z_u^β = ib
3. show that (z_(MM β²) /z_u ) = ((bb^β β 2Re(bz^β ))/(ibb^β ))
4. show that 2Re(b^β z_0 ) = bb^_ where
z_0 = ((z + z β²)/2)
5. Deduce that for M β (β³) , M is
a perpendicular bisector of [MM β²]
2
ans
0
cmts
zβ² = (1/2)(z+(1/z))
z and zβ² are complex numbers
show that z = 2e^(iΞΈ)
show that Mβ² describes a conic section
2
ans
0
cmts
h_a (x) = e^(βx) + ax^2
show that h_a admits a minimum in R
1
ans
0
cmts
u_(n+1) = u_n βu_n ^3 ; u_0 β ]0, 1[
. show that u_n β ]0, 1[
. show that u_n converges to 0
v_n = (1/u_(n+1) ^2 ) β (1/u_n ^2 )
. express v_n interms of u_n
. show that v_n converges to 2
f(x) = ((2βx)/((1βx)^2 ))
. show that f is increasing and deduce that
v_n is decreasing
. show that v_n β₯ 2
1
ans
0
cmts
Find inf{(m/n) β£ m, n β N, m<nβ2}
0
ans
1
cmts
Question 207390
1
ans
0
cmts
let f:RβR be a continuous function then
show that
(1) if f(x) = f(x^2 ) β x βR then f is a constant
function
(2) if f(x) = f(2x+1) βxβR then f is a
constant function
2
ans
0
cmts
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)
1
ans
0
cmts
If the nth term of a sequence is
given by ((n^2 β2n)/4) ,what is the sum of n
terms of the sequence?
1
ans
0
cmts
Question 206442
1
ans
0
cmts
Question 206151
1
ans
0
cmts
Question 206136
1
ans
0
cmts
write the following recursive function in explicit form
f(1)=1
f(n+1)=(n+1)f(n)+n!
1
ans
0
cmts
nature of the serie Ξ£_(nβ₯1) ((ln(n))/n)
1
ans
0
cmts
soit f: R^3 βR^3 f(x,y,z)=(x+y,2xβy,x+z)
β’1 Ecrire la matrice M de cette application
dans la base canonique B de R^3
β’2 Calculer f(1,2,3)de 2 manieres differentes
βen utilisant la definition de f
βen utilisant la matrice M
β’3 determiner bsse de Ker( f) et de Im(f)
β’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
β’5Calculer f(v_1 ) donner ses coordonnes(locus)
dans bass E
avec f(v_2 )=v_1 +6v_2 β4v_3
f(v_3 )=2v_1 +8v_2 β6v_3
β’6 Ecrire la matrice N de f dans base F
β’7 Retrouver cette matrice a partir de M
en utilisant la formule de changement de base
1
ans
0
cmts
let a , b >0 find all differentiable function
f:(0,β)β(0,β) such that
fβ²((a/x)) = ((bx)/(f(x))) , β x>0
0
ans
0
cmts
Question 204394
0
ans
0
cmts
Question 204393
0
ans
8
cmts
let ABC a given triangle. Can we find
three positions I,J,K on the side AB,AC,BC
Such that IJK is equilateral?
1
ans
0
cmts
f(x)={1+((βx^2 )/x) if x#0
2 if x=0
study the continuty of f in 0
3
ans
1
cmts
find the seauence u_n wich verify
u_0 =1 and u_n +u_(n+1) =(((β1)^n )/n)
for nβ₯1
3
ans
0
cmts
if f(β1)=f(0)=f(2)=0 and f(1)=6
then find f(x)=?
2
ans
0
cmts
f : RβR
f(xy)(f(x)βf(y))= (xβy)f(x)f(y)
1
ans
0
cmts
Question 201848
1
ans
0
cmts
f(x+1)βf(x)=3f(x)Γf(x+1)
D_f =N
2023Γf(1402)=1
have equation f(x)=1 solution?
0
ans
0
cmts
Question 200973
1
ans
1
cmts
Find all polynomials P(x) with
real coefficients such that for
all nonzero real numbers x,
P(x)+P((1/x))=((P(x+(1/x))+P(xβ(1/x)))/2)
1
ans
0
cmts
f : Rβ{0,1} β R
f(x)+f((1/(1βx)))= ((2(1β2x))/(x(1βx)))
for xβ 0 and xβ 1
0
ans
0
cmts
Give a function
f: Rβ(0;+β) continous on R and such that
f(x+y) = f(x).f(y)
a. Prove f(0) = 1
b. Let h(x) = ln[f(x)]. Prove that:
h(x+y) = h(x) + h(y)
c. Find all the function f such that problem request
1
ans
0
cmts
if f(x) is also differentiable on R such that
fβ²(x) > f(x) β x β R and f(x_0 ) = 0 then
prove that f(x) β₯ 0 β x > x_0
