Answers edited by Eddie

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• How do you find the antiderivative of #cos^4 x sin(2x) dx#?
  
• How do you find the limit of # 1/ x+e^(1/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?
  
• What is a solution to the differential equation #dy/dx=(x+y)/(x-y)#?
  
• Question #24b79
  
• What is a solution to the differential equation #dy/dx=(1+x)/(xy)# with y(1)=-4?
  
• What is a solution to the differential equation #sqrtx+sqrtyy'=0# with y=4 when x=1?
  
• How do you determine the limit of #sinh(2x)/e^(3x)# as x approaches infinity?
  
• How do you integrate # ln(sqrt(x)) #?
  
• What is a solution to the differential equation #dy/dx=(3y)/(2+x)#?
  
• Are there any equation for 2d motion and if present what are they?
  
• Find the volume of the region bounded by y=sqrt(z-x^2) and x^2+y^2+2z=12?
  
• Is there a difference between vibration and waves?
  
• Question #fe77f
  
• What is the equation of the normal line of #f(x)= x/sqrtsinx# at #x = pi/8#?
  
• What is a general solution to the differential equation #y'+2xy=2x^3#?
  
• How do you find all solutions to #x^3-(1-i)=0#?
  
• 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?
  
• How do you evaluate the integral #int e^(-absx)# from #-oo# to #oo#?
  
• How do you simplify #z^6 = a + bi# given #z = sqrt 3 + i#?
  
• What is a particular solution to the differential equation #dy/dx=cosxe^(y+sinx)# with #y(0)=0#?
  
• 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 the limit of #(sin²x)/(x)# as x approaches 0?
  
• How do you evaluate the integral #int x^1000e^-x# from 0 to #oo#?
  
• Question #46f42
  
• How do you find the definite integral for: #tln(t) dt# for the intervals #[1, 10]#?
  
• 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?
  
• What law defines the concept that an object in motion will continue in motion unless it experiences a net external force?
  
• How do you find the limit of #(sin2x)/x# as x approaches infinity?
  
• What is a general solution to the differential equation #dy/dx=10-2y#?
  
• How do you find the volume of the solid bounded by x^2+y^2=4 and z=x+y in the first octant?
  
• What is #f(x) = int x/sqrt(x^2-1) dx# if #f(3) = 0 #?
  
• What is #f(x) = int xsinx dx# if #f(pi/4)=-2 #?
  
• How do you integrate # (x-1) e^(-x^2+2x) dx#?
  
• How do you find the volume of the solid bounded by the coordinate planes and the plane #7x+y+z=4#?
  
• How do you convert #(y = 2 + x)# to parametric equation?
  
• How do you find the limit of # sin(7x)/x# as x approaches 0?
  
• What is a general solution to the differential equation #y'=2+2x^2+y+x^2y#?
  
• How do you evaluate the limit #(x/(x+2))^x# as x approaches #oo#?
  
• How do you differentiate #g(y) =(x-2x^2)e^(3-x) # using the product rule?
  
• 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#?
  
• Question #d78f0
  
• Question #a1395
  
• 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)?
  
• Question #ba5c4
  
• How do you implicitly differentiate #-1=(x+y)^2-xy-e^(3x+7y) #?
  
• A force field is described by #<F_x,F_y,F_z> = < xy +z , xy-x, 2y -zx > #. Is this force field conservative?
  
• How do you differentiate #cos(x^2)#?
  
• How do you find the definite integral of #2x* (x-3)^5 dx# from #[-1, 2]#?
  
• 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 power series for #f(x)=int t^2/(1+t^2)dt# from [0,x] and determine its radius of convergence?
  
• What is a solution to the differential equation #dy/dx=e^x/y# with y(0)=1?
  
• What is the derivative of #sqrtthetasintheta#?
  
• 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?
  
• 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?
  
• How do you find all solutions of the differential equation #(d^2y)/(dx^2)=3y#?
  
• How do you differentiate #f(x) = e ^ (2(e^(t) - 1)#?
  
• What is a solution to the differential equation #y'+y/x^2=2/x^3#?
  
• How do you evaluate the integral #int tan theta d(theta)# from 0 to #pi/2#?
  
• What is parametric equation of the line created by the intersecting planes x = 2 and z = 2?
  
• 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 integrate #int lnx/x^5# by integration by parts method?
  
• 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?
  
• What is the limit as x approaches 0 of #(2x)/tan(3x)#?
  
• What is a solution to the differential equation #dy/dx = 1 - 0.2y#?
  
• Using the limit definition, how do you find the derivative of #f(x) = x/(x+4)#?
  
• What is a solution to the differential equation #dy/dx=2yx+yx^2#?
  
• How do you find #(dy)/(dx)# given #lny=xe^x#?
  
• How do you find the limit of #(1)/(x-2) # as x approaches #2^+#?
  
• How do you find parametric equations for the line of intersection of two planes 2x - 2y + z = 1, and 2x + y - 3z = 3?
  
• Question #50cc1
  
• Given #(sin(-2x)) / x# how do you find the limit as x approaches 0?
  
• How do you differentiate #y= e^(1-x) #?
  
• 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?
  
• How do you find the arc length of the curve #y=x^2/2# over the interval [0, 1]?
  
• How do you find the limit of #x^(sin(x))# as x approaches 0?
  
• How do you find the power #(-2+2i)^3# and express the result in rectangular form?
  
• 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?
  
• Question #3b7a3
  
• Question #fb85a
  
• What is the derivative of #1/(1+x^4)#?
  
• How do you integrate #int xarcsinx^2# by parts from #[0,1]#?
  
• How do you determine if #f(x) = 2x^2 - 2# is an even or odd function?
  
• Question #d076b
  
• What is a solution to the differential equation #y'=3^-y(2x-4)# and y(5)=0?
  
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