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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