Answers edited by Eddie

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• What is a solution to the differential equation `dy/dx=(x+y)/(x-y)`?
  
• Question #fe77f
  
• Question #d78f0
  
• How do you integrate `int xarcsinx^2` by parts from `[0,1]`?
  
• How do you evaluate the limit `(x/(x+2))^x` as x approaches `oo`?
  
• How do you find the definite integral of `2x* (x-3)^5 dx` from `[-1, 2]`?
  
• A fence 4 feet tall runs parallel to a tall building at a distance of 2 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
  
• What is a particular solution to the differential equation `dy/dx=cosxe^(y+sinx)` with `y(0)=0`?
  
• How do you find the limit of `(sin2x)/x` as x approaches infinity?
  
• How do you integrate `int lnx/x^5` by integration by parts method?
  
• What is a solution to the differential equation `dy/dx=(3y)/(2+x)`?
  
• Question #50cc1
  
• How do you evaluate the integral `int e^(-absx)` from `-oo` to `oo`?
  
• How do you use the second fundamental theorem of Calculus to find the derivative of given `int 3/t^2 dt` from `[1,x]`?
  
• How do you find all solutions to `x^3-(1-i)=0`?
  
• How do you find `(dy)/(dx)` given `lny=xe^x`?
  
• How do you find the limit of `(sin²x)/(x)` as x approaches 0?
  
• The kinetic energy of an object with a mass of `2 kg` constantly changes from `8 J` to `136 J` over `4 s`. What is the impulse on the object at `1 s`?
  
• What law defines the concept that an object in motion will continue in motion unless it experiences a net external force?
  
• What is the limit as x approaches 0 of `(2x)/tan(3x)`?
  
• Let R be the region in the first and second quadrants bounded above by the graph of `y=20/(1+x^2)` and below by the horizontal line y=2, how do you find volume of the solid generated when R is rotated about the x-axis?
  
• From a unit sphere, the part between two parallel planes equidistant from the center, and with spacing 1 unit in-between, is removed. The remaining parts are joined together face-to-face, precisely. How do you find the volume of this new solid?
  
• How do you implicitly differentiate `-1=(x+y)^2-xy-e^(3x+7y)`?
  
• Question #24b79
  
• What is a solution to the differential equation `dy/dx=e^x/y` with y(0)=1?
  
• How do you differentiate `y= e^(1-x)`?
  
• How do you find the limit of `1/ x+e^(1/x)` as x approaches 0?
  
• What is a solution to the differential equation `y'+y/x^2=2/x^3`?
  
• Question #a1395
  
• What is a general solution to the differential equation `y'+2xy=2x^3`?
  
• How do you find the arc length of the curve `f(x)=x^3/6+1/(2x)` over the interval [1,3]?
  
• How do you differentiate `f(x) = e ^ (2(e^(t) - 1)`?
  
• How do you convert `(y = 2 + x)` to parametric equation?
  
• How do you evaluate the integral `int tan theta d(theta)` from 0 to `pi/2`?
  
• Question #ba5c4
  
• How do you find the antiderivative of `cos^4 x sin(2x) dx`?
  
• How do you differentiate `cos(x^2)`?
  
• How do you find the volume of the solid bounded by the coordinate planes and the plane `7x+y+z=4`?
  
• What is parametric equation of the line created by the intersecting planes x = 2 and z = 2?
  
• How do you find the power `(-2+2i)^3` and express the result in rectangular form?
  
• How do you find all solutions of the differential equation `(d^2y)/(dx^2)=3y`?
  
• Are there any equation for 2d motion and if present what are they?
  
• How do you find parametric equations for the line of intersection of two planes 2x - 2y + z = 1, and 2x + y - 3z = 3?
  
• How do you find the limit of `sin(7x)/x` as x approaches 0?
  
• What is a general solution to the differential equation `dy/dx=10-2y`?
  
• How do you find the arc length of the curve `y=x^2/2` over the interval [0, 1]?
  
• How do you find the power series for `f(x)=int t^2/(1+t^2)dt` from [0,x] and determine its radius of convergence?
  
• How do you simplify `z^6 = a + bi` given `z = sqrt 3 + i`?
  
• How do you determine if `f(x) = 2x^2 - 2` is an even or odd function?
  
• What is `f(x) = int x/sqrt(x^2-1) dx` if `f(3) = 0`?
  
• A force field is described by `<F_x,F_y,F_z> = < xy +z , xy-x, 2y -zx >`. Is this force field conservative?
  
• What is a solution to the differential equation `sqrtx+sqrtyy'=0` with y=4 when x=1?
  
• Question #46f42
  
• How do you integrate `(x-1) e^(-x^2+2x) dx`?
  
• How do you use the Fundamental Theorem of Calculus to find the derivative of `int (u^3) / (1+u^2) du` from 2-3x to 5?
  
• What is a solution to the differential equation `dy/dx=2yx+yx^2`?
  
• Let R be the shaded region in the first quadrant enclosed by the y-axis and the graphs of `y=4-x^2` and `y=1+2sinx`, how do you find the volume of the solid whose base is R and whose cross sections perpendicular to the x-axis are squares?
  
• Question #fb85a
  
• How do you use the Fundamental Theorem of Calculus to find the derivative of `int sqrt(1+ sec(t)) dt` from x to pi?
  
• How do you find the definite integral for: `tln(t) dt` for the intervals `[1, 10]`?
  
• How do you determine the limit of `sinh(2x)/e^(3x)` as x approaches infinity?
  
• Question #d076b
  
• What is a general solution to the differential equation `y'=2+2x^2+y+x^2y`?
  
• Is there a difference between vibration and waves?
  
• How do you use the limit definition to find the slope of the tangent line to the graph `f(x) = sqrt(x+1)` at (8,3)?
  
• What is `f(x) = int xsinx dx` if `f(pi/4)=-2`?
  
• How do you differentiate `g(y) =(x-2x^2)e^(3-x)` using the product rule?
  
• How do you find the limit of `x^(sin(x))` as x approaches 0?
  
• How do you find the power series for `f(x)=int(ln(1+2t^2)dt` from [0,x] and determine its radius of convergence?
  
• How do you find the limit of `(1)/(x-2)` as x approaches `2^+`?
  
• What is a solution to the differential equation `y'=3^-y(2x-4)` and y(5)=0?
  
• What is the equation of the normal line of `f(x)= x/sqrtsinx` at `x = pi/8`?
  
• What is the derivative of `1/(1+x^4)`?
  
• How do you find the volume of the solid bounded by x^2+y^2=4 and z=x+y in the first octant?
  
• Using the limit definition, how do you find the derivative of `f(x) = x/(x+4)`?
  
• Question #3b7a3
  
• A harmonic oscillator of mass 60 g has a period of 10 seconds. What should the mass be in order to reduce the period to 5 seconds?
  
• What is a solution to the differential equation `dy/dx=(1+x)/(xy)` with y(1)=-4?
  
• Consider the curve defined by the equation `y+cosy=x+1` for `0≤y≤2pi`, how do you find dy/dx in terms of y and write an equation for each vertical tangent to the curve?
  
• How do you evaluate the integral `int x^1000e^-x` from 0 to `oo`?
  
• Find the volume of the region bounded by y=sqrt(z-x^2) and x^2+y^2+2z=12?
  
• How do you integrate `ln(sqrt(x))`?
  
• Given `(sin(-2x)) / x` how do you find the limit as x approaches 0?
  
• What is a solution to the differential equation `dy/dx = 1 - 0.2y`?
  
• What is the derivative of `sqrtthetasintheta`?
  
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