Answers edited by MoominDave

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• Who's interested in a new Socratic on a different website?
  
• What is the arc length of #f(x)=cosx# on #x in [0,pi]#?
  
• Prove that the volume of any paraboloid is always half the volume of the circumscribed cylinder?
  
• Use the instantaneous rate of change of #f(x) = e^(5x)# to find the equation of the tangent line to f(x) at x = 0?
  
• What is the domain and range of #f(x) = (x+3)/(x^2+4)#?
  
• What are the local extrema, if any, of #f(x)= (4x-3)^2-(x-4)/x #?
  
• What is the slope of the line normal to the tangent line of #f(x) = secx+cos^2(2x-pi) # at # x= (11pi)/8 #?
  
• How do you find the inflection points of #f(x)= 12x^5+45x^4-80x^3+6#?
  
• Lim x^alfa* (cosx/x)^2, at infinity. Alfa can take any value we want . Who can demonstrate that this integral is convergent?
  
• How do you factor #f(x) = x^4 + 4x^3 - 3x^2 +40x + 208#?
  
• What are the asymptote(s) and hole(s), if any, of # f(x) =(x^2-2x+1)/(x*(x-2))#?
  
• How do you simplify #sqrt(3-2*sqrt(2))#?
  
• How do you find an expression for #sin(x)# in terms of #e^(ix)# and #e^(ix)#?
  
• How do you factor #8a^3+27#?
  
• Find the solution to the system of equations Log (2000xy) minus log(x).log y=4 Log(2yz)minus log y.logz=1 Log(zx) minus log(z).logx=0 Base of log is 10 everywhere?
  
• How do you solve #(x + 4) ^ { 3} - 8= x ( x + 5) ( x + 7) - 5#?
  
• Let #a,b,c# be positive real numbers such that #a+b+c=1#.Prove the following inequality: #(a+1/a)^2+(b+1/b)^2+(c+1/c)^2>=100/3#?
  
• How do you integrate #int x^3/sqrt(x^2-2x+10)dx# using trigonometric substitution?
  
• Suppose a person weighs 100 pounds. If he travels to a planet with 5 times the mass of Earth and 10 times the radius of Earth, what will his new weight be?
  
• What's the square root of 8100?
  
• How to I solve homogeneous equation of #y dy/dx +x=2y# ?
  
• What are the points of inflection of #f(x)=1/(5x^2+3) #?
  
• Given a fair 12-sided dice: If the dice is rolled ten times, what is the probability of rolling exactly two 6s?
  
• How do you differentiate #y = (ln(x^2))^(2x+3)#?
  
• An angle exceeds the measure of its supplement by 40degree .what is the measure of the supplement?
  
• Please solve q 16?
  
• How do you factor #y=-2x^3-6x^2+8x+24 #?
  
• On ground the gravitational force on satalite is W what is the gravitational force when the satellite is at the height of R/50 (R is radius of Earth)?
  
• How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n))/((2n+1)!)# from #[1,oo)#?
  
• How do you integrate #int 1/sqrt(4x^2+16x+8) # using trigonometric substitution?
  
• Thoughts on the recent announcement made about the future of the Socratic website? Share them here!
  
• 1) What is the arc length of C? 2) The surface of revolution on the x axis?
  
• Why do you factor quadratic equations?
  
• How to solve? ln(x)=2/x-2
  
• How do you factor #x^3-12x^2+41x-42#?
  
• How to solve the values of t?