Answers created by Cesareo R.

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• What is the significance of partial derivative? Give an example and help me to understand in brief.
  
• Does the series #sum_{n=1}^oo (5n)^(3n)/(5^n+3)^n# diverge or converge?
  
• Solve this inequality? #(x+1)^2 - abs(x-2) >= 0#
  
• #lim_(x->0)(e^x-1)/sin(2x)=# ?
  
• Question #c229d
  
• What is the coefficient?
  
• Solve the inequality plASE ?
  
• Solve the system of equations please?
  
• How do i solve part (b) of this question?
  
• Power series help?
  
• How do you determine if the series the converges conditionally, absolutely or diverges given #sum_(n=1)^oo (cos(npi))/n^2#?
  
• Please help with this physics problem?
  
• #int\ e^(-7x)*cos(2x)dx =# ?
  
• How do you solve #x-2y<8# and #2x-3y<=6#?
  
• #lim_(n->oo)(9*9^(1/3)*9^(1/9)*9^(1/27)*......*9^(1/(3^n))# ?
  
• Given that #lim_(x->oo)((x^2)/(1+x)-ax-b)#, find the values of #a# and #b# ?
  
• These statements are true or false?Please justify your answer.(i)The function #f(x,y)=(x³y+1,x²+y²)# is locally invertible at#(1,2)#.(ii)The function #f(x,y)=x³+y³# is integrable on #[1,2]×[1,3].#
  
• If p is the length of the perpendicular from the origin to the line #x/a+y/b=1#,prove that #1/(p²)=1/(a²)+1/(b²)#?
  
• #lim_(x->oo)((x-1)/(x+1) )^x =# ?
  
• Find the domain and range of the function #f# defined by #f(x,y)=(3x^2y^2)/(x^2+y^4)# ?
  
• Find #f@g# and #g@f# ,if they exist,for the functions #f(t)=4t,t∈RR,g(x,y)=x+y,x,y∈RR #?
  
• Find the mass of an object which is in the form of a cuboid#[0,1]×[2,4]×[1,3]#.The density at any point #(x,y,z)# on the cuboid is given by #delta(x,y,z)=x^2+y^2+z^2# ?
  
• Find a Cartesian Equation of the plane with contains the line #(x-2)/3=(y+4)/2=(z-1)/2# and passes through the point #(1,1,1)#?
  
• How can I solve this differential equation? : #(2x^3-y)dx+xdy=0#
  
• Check whether the function #f(x,y)={(6xy)/sqrt(x^2+y^2) " if " (x,y)≠(0,0), {0 if (x,y)=(0,0)# is continuous at the origin?
  
• Let #f(x,y)={(x²y)/(x⁴+y²), " if " x⁴+y²≠0, {0, " if " x=y=0#. Check whether #lim_((x,y)→(0,0))f(x,y) # exists or not?
  
• Triangle abc is inscribed in a circle. Point P lies on the circumscribed circle of triangle ABC. Through P, PN, PM and PL are Perpendiculars on the sides of the triangle as shown in the figure. Prove that N,M,Lare collinear?
  
• Two blocks of masses #m_1# and #m_2# are connected with a light spring of force constant #K# and whole system is kept on a frictionless horizontal surface the masses are applied forces #f_1# and #f_2# respectively?
  
• A particle projected at a definite angle #alpha# to the horizontal passes through points #(a,b)# and #(b,a)# referred to horizontal and vertical axes through the point of projection. Then?
  
• Evaluate the integral of f(x,y,z)=x+z-3 over the cylinder bounded by x²+y²=1,z=0 and z=1?
  
• How do you find a power series representation for # f(x)= 9/(1-3x)^2 # and what is the radius of convergence?
  
• These statements are true or false?Please justify your answer.(i)#lim_(x→0)(1/(x²)-1/(sin²x))# is in #(0/0)# form.(ii)Domain of #f(x,y)=(xy)/(x⁴+y⁴)# is #R²#.
  
• Prove that #P(barA//B) = 1-P(A//B)#?
  
• This statement is true or false?Please justify your answer. #f(x,y)=sin((x²y)/(x³+y³))/(ln(x+y/x))# is a homogeneous function of degree 2.
  
• How to prove #ab+cd<=sqrt((a^2+c^2)(b^2+d^2))# given a, b, c, d, are any four positive numbers?
  
• Exists some #x# for which #sum_{k=0}^oo [log(-x)]^-k# converges, and what is the sum?
  
• A particle has initial velocity, #v = 3hati + 4hatj# and a constant force #F = 4hati - 3hatj# acts on it. The path of the particle is?
  
• Question #b1a21
  
• Let #bbx=bbe_1+bbe_2-2bbe_3# and #bby=2bbe_1-bbe_2+bbe_3#,where #bbe_1,bbe_2,bbe_3# are unit vectors. Find #|bbx+2bby|# and #|bbx+bby#|?
  
• Find two level curves of the function #f(x,y)=(x+y)/(x-y),x≠y# and sketch them?
  
• Show that the functions #f(x,y)=ln x-ln y # and #g(x,y)=(x^2+2y^2)/(2xy)# are functionally dependent?
  
• Please help?
  
• Number of real solutions of the equation #log_10(-x) = sqrt(log_10sqrt(x^2))#?
  
• The sum #1 + 3 + 7 + 15 + 31 ...# to #100# terms is?
  
• Whatever be the value of theta, prove that the locus of the point of intersection of the straight lines #y=xtan(theta)# and #xsin^3(theta)+ycos^3(theta)=asin(theta)cos(theta)# is a circle.find the equation of the circle?
  
• How to solve for #inte^xcosxdx# ?
  
• How to choose two numbers for which the sum of their square roots is minimal, knowing that the product of the two numbers is #a#?
  
• Question #32022
  
• Every polynomial with complex coefficients can be written as the product of linear factors. Enter the linear factors of #P(z)=1+z+⋯+z^6+z^7# any help?
  
• For complex numbers z and #omega#, prove that #|z|^2omega -|omega|^2z = z - omega# if and only if #z = omega# and #z. baromega = 1#?
  
• If #x# is nearly equal to one, then find the approximate value of #{mx^m-nx^n}/{m-n}#?
  
• #lim_(n->oo)(((2n-1)!!)/(2n!!)) #?
  
• Given #x^3 - x y^2 + y^3 - 1=0# determine the points where #dy/dx = 0# ?
  
• If z = x + iy is a complex number, then sketch the set of points that satisfy the following equations?
  
• Question #4bc5b
  
• Find y' ?? Help
  
• Check whether or not the conicoid represented by #5x^2+4y^2-4yz+2xz+2x-4y-8z+2=0# is central or not. If it is, transform the equation by shifting the origin to the center. Else, change any one coefficient to make the equation that of a central conicoid.?
  
• Question #6edb0
  
• Are there polynomial functions whose graphs have: 11 points of inflection, but no max or min ?
  
• Evaluate the limit #lim_(x->0) (e^x+3x)^(1/x) #?
  
• Question #672ae
  
• Consider the basis #e_1 = (−2,4,−1)#, #e_2 = (−1,3,−1)# and #e_3 = (1,−2,1)# of #R^3# over #R#. Find the dual basis of #{e_1, e_2, e_3}#.?
  
• Mathematical induction question 1E plz I am stuck?
  
• What values of #c# in the equation #|2x+1|=x+c# give exactly two solutions?
  
• Prove that this converges to 0:#(prod_(k=1)^n(lambdak+a)/(lambdak+b)),0<=a<b,lambda>0,n=1,2,3......#?
  
• How to calculate sum of this? #sum_(n=1)^oo(-1)^n n(n-1)x^n#
  
• How to solve?
  
• Calculate the following limit #lim_(x->0) (a^x - b^x)/x#? The answer should be #log(b/a)#.
  
• Solve #e^x+x+1=0# ?
  
• Prove that there is no function #f# defined in #RR# for which it applies helpp?:(
  
• Proof of the shortest distance from a point to a plane formula?
  
• Find the set of real value(s) of #a# for which the equation |#2x+3#| + |#2x-3#| = #ax + 3# has more than two solutions. ?
  
• Calculate #sum_(n=0)^oo sqrt(n+3)+sqrtn-2sqrt(n+2)# ?
  
• How to prove that #7*25^n+2*6^(n+1)# divides 19?
  
• Which is bigger: # ( 1 + \sqrt{2} )^{ 1 + \sqrt{2} + 10^{-9,000} } # or # ( 1 + \sqrt{2} + 10^{-9,000} )^{ 1 + \sqrt{2} } # ? If your calculator could actually handle this -- please put it away !! :)
  
• Question #802ec
  
• Solve #cos^4(a)-sin^2(a)=1# ?
  
• How do you answer this question?
  
• Find the equation of the cone whose vertex is at the origin and base is the circle #x=a#, #y^2+z^2=b^2#?
  
• Anybody, please help me. This is a piecewise function?
  
• Question #37d69
  
• Find #sum_(n=1)^oo n^2/3^n = # ?
  
• Suppose # s(x) # and # c(x) # are 2 functions where: 1) # s'(x) = c(x) # and # c'(x) = -s(x); # 2) # s(0) = 0 # and # c(0) = 1. # What can you say about the quantity: # \qquad [ s(x) ]^2 + [ c(x) ]^2 # ?
  
• If #|Z - 4/Z| = 2#, then the maximum value of #|Z|# is equal to?
  
• How to find the maximum income? (See picture)Thanks!
  
• The remainder when x^(2011) is divided by x^2 -3x+2 is ?
  
• Question #9079e
  
• Determine which of the following definite integral equals #lim_{n\to infty} \Sigma_{i=1}^n 1/nsqrt{i/n}#?
  
• What is #1^2+(1^2+2^2)+(1^2+2^2+3^2)+...+(1^2+2^2+...+22^2)# ?
  
• Help me to solve this problem of limit please?
  
• Wave Question?
  
• What is the maximum profit? Thanks!
  
• Is the actual minimum of a graph still considered a relative minumum?
  
• Solve #|z-w|=|z+w| # ?
  
• Let #Z_1,Z_2# be complex numbers with #|Z_1| = |Z_2| = 1#, prove that #|Z_1 + 1| + |Z_2 +1| +|Z_1Z_2 +1| >=2#?
  
• How to resolve [x+1]=2x-1?
  
• Question #9ca46
  
• Calculate #lim_(n->oo)sum_(k=1)^n n/(n^2+k^2) =# ?
  
• Solve for x, y and z?
  
• Show that if the polynomial #f(x)=ax^3+3bx^2+3cx+d# is divided exactly by #g(x)=ax^2+2bx+c#, then #f(x)# is a perfect cube, while #g(x)# is a perfect square?
  
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