Questions asked by Raul

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Can you help me with this problem: $sinx+cosx=sinxcosx$ ? Please?
$X_(n+1)-aX_n+2=0$ Which are the set values of "a" for the string "Xn" is descending?
how you solve: $lim_(n->oo)(2-sqrt2)(2-root(3)2)(2-root(4)2)...(2-root(n)2))$ ?
How do you solve: $lim_(n->oo)(ln(1+e^(2n)))/(ln(1+e^(3n)))$ ? Thanks!
How you solve this? $lim_(n->oo)prod_(k=1)^n((k+1)^2)/(k(k+2))$
How you solve this? $lim_(n->oo)sum_(k=1)^n1/((k+1)sqrt(k)+ksqrt(k+1)$
How you solve this?: $lim_(n->oo)sum_(k=1)^n(2k+1)/(k^2(k+1)^2)$
How you slove this? $lim_(n->oo)cos(pisqrt(4n^2+n+1))$
How you solve this? $lim_(n->oo)(|__x__|+|__3^2x__|+...+|__(2n-1)^2x__|)/n^3$
How you solve this? Solve in $ZZ_6$ equation: $hat(x)^3=hatx$
How you solve this ? $lim_(n->oo)(5^(n)n!)/(2^(n)n^n)$
How you solve this? to solve and discuss after real parameter "a" the equation: $sinx+asin2x+sin3x=0$
How to solve this? $sinx+sin2x+sin3x=0$
How you solve this? $4^x+9^x+25^x=6^x+10^x+15^x$
How to solve this inequation? $sin^4x+cos^4x>=1/2$
How to solve this? If in the Ring (A,+,*) the equation $x^2+1=0$ has unique solution demonstrate that 1+1=0,where "1" is unit element of the ring.
How to solve this? Find $m in RR$ for which $X^3-3X+m=0$ has a double root.
How to calculate this limit? f:[0,1] $->RR$ ,f(x)=x $sqrt(1-x^2)$ Calculate $lim_(x->0)1/x^2int_0^xf(t)dt$
How to solve this? $4^x+9^x+25^x=6^x+10^x+15^x$
A={1,2,3,4,5,6};How many bijective functions $f:A->A$ have the property that $f(1)!=2$ ?
How to solve this? $f=(2x^2-x-1)^10$ Calculate $x_1+x_2+x_3+...+x_20$ .
$P in NN$ \{0,1}; $q>0$ ;how to solve limit? $lim_(n->oo)(qn+1)/(qn)*(qn+p+1)/(qn+p)*...*(qn+np+1)/(qn+np)$
How to calculate this limit? $lim_(n->oo)sum_(k=1)^n(1/2^k+1/3^k)$
How to calculate limit? $lim_(n->oo)sum_(k=0)^n(C_n^k)/(2n)^k$
How to solve this limit? $lim_(n->oo)(1+x^n(x^2+4))/(x(x^n+1))$ ;x>0
How to calculate this limit? $lim_(n->oo)prod_(k=1)^ncos(2^(k-1)x);x!=kpi$
How to solve this? Determine the continuity and derivability domain for $f(x)$ $f:[0,oo)->RR,f(x)=|x-1|sqrtx$
How to find $B^(-1)$ ?;We know that $B^2=B+2I_3$
How to demonstrate that $sqrt(2)^(sqrt(3)-1)>sqrt(3)^(sqrt(2)-1)$ ?We know that $g:(1,+oo)->RR,g(x)=$ $(lnx)/(x-1)$ ,and $g$ is decreasing.
We have $DeltaABC$ and the point M such that $vec(BM)=2vec(MC)$ .How to determinate x,y such that $vec(AM)=xvec(AB)+yvec(AC)$ ?
$a in(pi,(3pi)/2);sina=-4/5;$ How to calculate $tga/2$ ?
$f:M_2(RR)->M_2(RR);f(X)=AXA^(-1);A inM_2(RR);A-$ inversable;How to demonstrate that $f$ is an bijective function?
How to find $a$ ,such that $BC=I_3$ ?; $A=((1,3,2),(3,9,6),(2,6,4));B=I_3+A;C=I_3+aA;a inRR$
How to determine the coordinates of the point M? $A_(((2,-5)));B_(((-3,5)))$ ;And $vec(BM)=1/5vec(AB)$
How to solve this equation? $2cosx+1=0;x in[0,3pi)$ ;
How to calculate this integral? $int_0^1x2^xdx$
$f:RR->RR;f(x)=e^x-x-1;g:[0,1]->RR;g(x)=f(x)+x$ .How to calculate the volume of the body obtained by rotating the graph of the function "g" axis OX?
Hoe to solve this?We have $hat3 inZZ_7$ ;Calculate $hat3^6$ and $hat3^2014$
How to solve this? $f:RR$ \{2} $->RR;f(x)=x^2/(x-2)$ .Demonstrate that $8<=int_3^4f(x)dx<=9$
How to calculate this? $ointxdx$
How to solve this? We have the ring $(ZZ_8,+,*)$ Demonstrate that the invertible elements of this ring are: $hat1,hat3,hat5,hat7$ .
How to solve this?If a $in ZZ_8$ is an invertible element,demonstrate that $hat2x=a$ don't have solutions $x in ZZ_8$
How to solve this? If $b in ZZ_8$ is an non-invertible element,demonstrate that $hat2x=b$ have exactly two solutions $x in ZZ_8$ .
How to solve this limit? $lim_(x->oo)(xa^(x+1)+1);ain(0,1)$
How to solve this?We have $M_2(ZZ_3)$ second order matrix set with elements of $ZZ_3$ .Determine the number of elements of the set $M_2(ZZ_3)$ .
How to solve this?We have $O_(((0,0))),A_(((3,4))),B_(((x,y))).$ Determine real numbers $x,y$ such that $Delta_(OAB)$ be equilateral.
How to demonstrate this?We have equilateral trinagle $DeltaOAB$ : $O_(((0,0))),A_(((m,n)));m,ninNN;m,n!=0$ and $B_(((x,y)));x,yin(0,oo)$ .Demonstrate that $B$ can not have both coordinates natural numbers.
How to solve this equation in $[0,2pi]$ ? $min{sinx,cosx}=pi/4$ .
How many subsets with three elements of $A={1,2,3,4,5,6}$ containing element "1"?
We have $f:[0,2]->RR,f(x)=sqrt(4-x^2)$ .How to solve this limit? $lim_(x->0)1/x^2int_0^xtf(t)dt$
We have $f:RR->RR,f(x)=(x+2)e^(-|x|)$ How to solve this limit? $lim_(x->0)(f(x)-f(0))/(x);x>0$
We have $f,ginRR[X];f=(X-1)^n-X^n+1;g=X^2-3X+2$ .How to find the rest of dividing $f$ to $g$ ?
We have ${(x+y+z=0),(2xcosalpha+2ysinalpha+z=0),(2xcos2alpha-2ycos2alpha-z=0):}$ ;How you solve this for $alpha=(61pi)/6$ ?
We have $f:RR->RR,f(x)=e^(x-1)$ .How to demonstrate that $f(x)>x,$ for any $x inRR$ \{1}?
We have $f:RR->RR,f(x)=e^(x-1),$ and the string $(X_n)_(n>=1)$ with ${(x_1=2),(x_(n+1)=f(x_n)):}$ .How to demonstrate that ( $X_n$ ) is strictly monotone?
How to solve this equation in $RR$ ? $2sin^2x-sqrt(3)sin2x=0$
How many numbers with three distinct digits have digits from {1,2,3,4,5} and a digit is 3?
We have $g:RR->RR$ a continous function with property that $int_(-x)^xg(t)dt=0$ for each $x inRR$ .How to demonstrate that g is an odd function?
If function $f:RR->RR$ have one parity (even or odd) then hers derivate have the opposite parity?
How to demonstrate that $int_(-a)^af(x)dx=0$ for $f$ -odd?
We have $f:RR->CC$ *, $f(x)=cos(2xpi)+isin(2xpi)$ .How to demonstrate that $f$ is not surjective?
We have triangle $ABC$ with $BC=13,AC=14,hat(C)=arccos(5/13)$ .How to find the other two angles?
We have triangle with $AB=6,hat(A)=pi/3 and hat(B)=pi/4$ .How to find $AC and BC$ ?
How to verify if the groups $(RR,+)$ and $(CC$ * $,*)$ are isomorphic?
In the plane of the triangle $ABC$ we have $P$ and $Q$ such that $vec(PC)=3/2vec(BC)$ and $vec(AQ)=1/4vec(AC)$ ,and $C'$ is the middle of $[AB]$ .How to demonstrate that $P,Q$ and $C'$ are collinear points with theorem of Menelaus?
We have $f:RR->RR,f(x)=|x|root(3)(1-x^2)$ .How to find maximum domain of differentiability?
We have $f:RR->RR,f(x)=|x|root(3)(1-x^2)$ .Is this function continous in $x=0$ ?
How to demonstrate this with mathematical induction? $P(n):n^3+5n$ divide with 6 is true $forall ninNN$ .
How to calculate this? $sin^2(110^@)+sin^2(200^@)$ .
If we have $f:{a,b,c}->{1,2,3,4,5}$ .What is the number of bijective functions?
How to calculate this? $lim_(x->oo)(ln((x+2)/x)-ln((x+1)/(x-1))+1)$
What are the values of $m$ for which inequality is true? $(m+2)e^(-2x)+2(m+2)e^-x+m>0$ .
How you factorize this? $abs((4,4,m),(6,m,3),(m+3,3,4))$
How to determine height of the cylinder with maximum volume engraved in a sphere with radius $R$ ?
How to calculate this? $abs((4,4,m),(6,m,3),(m+3,3,4))$
How ro solve this? $arccosx>arccosx^2$ .
We have $G=(1,2)$ and $x@y=(3xy-4x-4y+6)/(2xy-3x-3y+5)$ .How you find $uin G$ such that $x@u=x$ ?
We have $f:(0,oo)->RR;f(x)=(x+a)/(x+b);a,binRR$ .How you verify if $f$ is a bijective function?
Having function $f:(0,oo)->RR,f(x)=xlnp-plnx,p inRR;p>0$ ,how to find $p>0$ sush that $f(x)>=0,forall x in(0,oo)$ ?
In triangle $ABC$ we have $M$ the middle of $[BC]$ .How to demonstrate that $vec(AB)+vec(AC)=2vec(AM)$ ?
How to solve this equation? $cosx+sqrt(3)sinx=a^2;x inRR$ ,and for what values of $a$ ,the equation has solutions?
Having this function, $f:(0,oo)->RR;f(x)=xlogp-plogx;p inRR,p>0$ how to demonstrate that $e^x>=x^e forallx in(0,oo)$ ?
How you calculate this? $[1-sqrt2]+{sqrt2-1}$ .
How you calculate this? $abs((a,a+1,a+2),(a+1,a+3,a+1),(a+2,a+1,a))$
If a function admits horizontal asymptote at $-oo$ but at $+ oo$ does not admit,she can admit oblique asymptote to $+ oo$ ?
How to solve this equation? $arctg(x)+arctg(1/x)=pi/2$ ?
How you demonstrate that $C_n^0-C_n^2+C_n^4-C_n^6+...=2^(n/2)cos((npi)/4)$ ?
We have $f=X^n-4X^2+X+1$ .How to determine the rest of the division of $f$ to $g=(x-1)^2$ ?
We have $f=X^3-3X^2+1$ ;How to find $x_1^(-4)+x_2^(-4)+x_3^(-4)$ ?; $x_1,x_2,x_3$ are roots of $f(x)=0$ .
How to calculate this? $lim_(x->0)(ln(1+7x^2)/(7x^2)-ln(1+2x)/(2x))$ ; $x>0$ .
How you calculate this? $int_1^ndx/(x+|__x__|)$
How to calculate this? $int_(1/(n+2))^(1/n)[1/x]dx$ .
We have $F:RR$ * $->RR$ such that $F'(x)=1/x,F(-1)=1,F(1)=0$ .How to calculate $F(e)+F(-e)$ ?
How you calculate this? $int_0^1sqrtx/((x+3)sqrt(x+3))$ , Using substitution of $sqrt(x/(x+3))=t$ .
We have $f:RR->RR;f(a)=int_0^1abs(x-a)dx$ .What is minimum value of the function $f$ ?
How you calculate this? $int_0^2(2x^3-6x+9x-5)/(x^2-2x+5)^n$ .Suggestion:Forming an odd function by substitution $x-1=t$ ,like $int_(-1)^1f(t)dt=0$ .
How to calculate this? $int_0^3sqrtx/(sqrt(x)+sqrt(3-x))$ .
If $P:RR->RR$ verify this equality: $P(1)+...+P(n)=n^5;n=1,2,...$ ,then how to find value of $int_0^1P(x)dx$ ?
How to calculate this? $int_0^(2pi)sin(mx)cos(nx)dx$ ; $m,n in ZZ$ .
How to calculate this? $lim_(x->oo)1/x int_0^xdt/(2+cost)$ .
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