Answers edited by Bill K.

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• A conical cup of radius 5 cm and height 15 cm is leaking water at the rate of 2 cm^3/min. What rate is the level of water decreasing when the water is 3 cm deep?
  
• How do you verify that the hypothesis of the Mean-Value Theorem are satisfied on the interval [2,5], and find all values of c in the given interval that satisfy the conclusion of the theorem for #f(x) = 1 / (x-1)#?
  
• How do you use chain rule to find partial derivatives?
  
• Question #dbcb0
  
• How do you find the first, second derivative of #3x^(2/3)-x^2#?
  
• Question #faf07
  
• How do you use the second derivative test how do you find the local maxima and minima of #f(x) = 12 + 2x^2 - 4x^4#?
  
• How do you find the slope of the tangent line to the curve #6x^2 - 2xy + 3y^3 = 216# at the point 6,0?
  
• How do you test for convergence: #int (((sin^2)x)/(1+x^2)) dx#?
  
• How do you verify that #y = x^3 + x - 1# over [0,2] satisfies the hypotheses of the Mean Value Theorem?
  
• How do you integrate #(sin x)/(1+sin x)^2#?
  
• How do you find the derivative of #(sqrt(x^2-x+1)-1)/(1+ sqrtx)#?
  
• How do you differentiate #xy^2 + xy = 12#?
  
• How do you find the point on the line #y=4x + 7# that is closest to the point (0,-3)?
  
• How do you use partial fraction decomposition to decompose the fraction to integrate #(6s^3) /(s^(4) - 5s^(2) +4)#?
  
• How do you determine the multiplier for exponential growth and decay?
  
• What are some algorithms used to find square root(or to approximate them)? Say #sqrt(2), sqrt(7)#
  
• What is a mathematical limit?
  
• What is the domain of the composite function #(g@f)(x)#?
  
• How do you find the taylor series series at #a=-3# of #f(x) = x - x^3#?
  
• Can Newton's Law of Cooling be used to describe heating?
  
• What is the difference between an antiderivative and an integral?
  
• What is the definition of an infinite sequence?
  
• How do you find the integral of #e^(x^2)#?
  
• Question #56b43
  
• How do you rationalize the denominator for #5/(sqrt6+sqrt5)#?
  
• How do you solve #ln (x+5) = ln (x-1) - ln (x+1)#?
  
• How do you factor by grouping #35xy-5x-56y+8#?
  
• What is the volume of the solid given the base of a solid is the region in the first quadrant bounded by the graph of #y=-x^2+5x-4^ and the x-axis and the cross-sections of the solid perpendicular to the x-axis are equilateral triangles?
  
• What is the Taylor Series Expansion for #sin(sin(x))#?
  
• How do you find the point on the the graph #y=sqrtx# which is plosest to the point (4,0)?
  
• How do you find the extrema of #f(x)=4 x^3-26 x^2+16x+1# on [0,3]?
  
• How do you find the limit of #x*sin(1/x)# as x tends to positive infinity?
  
• How do you use the Mean Value Theorem to solve #f(x)=x - sqrtx# on the closed interval [0,4]?
  
• How do you differentiate #sqrtt*(1-t^2)#?
  
• How do you differentiate #y=sqrtx#?
  
• How do you graph the inequality #2x + 3y > 6#?
  
• What is the average value of the function #1/x# between x=2/3 and x=8/3?
  
• Question #24b6e
  
• How do I integrate with Euler's method with a calculator or computer?
  
• How do you integrate #int(dx/(sqrt(2x^3 + 2x + 5)))#?
  
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