Questions asked by Neo

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• Let f(x,y)=xe^y -ye^x The gradient of f at (0,0) is ∇f(0,0)=?
  
• Using implicit differentiation, we can obtain the tangent line to the curve sin x+cos y=1 at point (π/2,π/2), i. e. =?
  
• Suppose y=3x-7 and x>=0. Then, the minimum value of (x^2)*y is?,and the maximum value of (x^2)*y is?
  
• F(x,y)=3(x^2)y+2y^3-3xy Find the relative extrema and saddle points?
  
• Suppode f(x)=cx^2+2x,if x<2.and 2x+4,if x>=2. f(x) is continuous on(-∞,∞).Then the value of c is?
  
• Function f(x)=(x^3)(e^x) is strictly increasing on the interval of?
  
• F(x)=x^1/2 Find the Taylor series of f(x) at 1?
  
• (ln^2 x)/x integral from 1 to e^2 is?
  
• Evaluate #int_0^4 ##int_(sqrtx)^2 sqrt(1+y^3) dydx#=?
  
• How to prove ?
  
• The radius of convergent of the power series #sum_ (n=1)^oo x^n/(n*2^n)# is?
  
• Given p>0,the series of#sum_ (n=1)^oo p^n*n^p# will diverge when the values of p is?
  
• Let #f(x)=|x^2-1|/(x-1)#. Then, #f# has a local maximum at #x#=?
  
• Evaluate the integral?
  
• #int_e^oo(1-lnx)/x^2 dx#=?
  
• #int int_R e^(-(xy)/2)dA# where #R#:the region bounded by #y=1/4x,y=2x,y=1/x,y=4/x# Evaluate integrals?
  
• #g(x)=(x-1)/(x+1), x=(z+1)/(1-z) #.Then#(dg)/dz=#?(Express it in z)
  
• The value of #lim_(h→0)1/hint_2^(2+h)sin(x^2)dx#is?