Answers created by Frederico Guizini S.

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• Using the method of undetermined coefficients,find the general solution of the DE y^(iv)-2y'''+2y''=3e^(-x)+2e^(-x)x+e^(-x)sinx?
  
• How do you find the volume of the region bounded by is revolved about the y-axis?
  
• Find the maximum, minimum, and inflection points for the following function ? y = #(x-1)^4(x+2)^3#
  
• How do you find the critical points f=x√(1+y)+y√(1+x)?
  
• What are the extrema and saddle points of #f(x,y) = x^2y+y^3x -1/x^3 + 1/(xy^2)#?
  
• What is #int (-x^3+9x-1 ) / (-2x^2+ 3 x +5 )#?
  
• How do I find the relative extrema of this function?
  
• The region under the curves #y=3/4x, y=1-x, y=x-1/x# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?
  
• How do I find the area bounded by the given curve, the x-axis and the given vertical lines?
  
• Can you help me determine the critical points of the given function and classify it as maximum or minimum?
  
• Let there be the function #f(alpha)= (L( v_a - v_0 sin alpha))/(v_0 cos alpha)# Where #L# ,#v_a# and #v_o# are constants. Determine #alpha# such that #f(alpha)# is minimal ?
  
• The given curve is rotated about the y-axis. Find the area of the resulting surface? y = 1/3 x^3/2, 0 ≤ x ≤ 21
  
• What are the points of inflection, if any, of #f(x)= (x-3)/sqrt(x^5-x^3-3x+4) #?
  
• What are the absolute extrema of #f(x)=(x-3)/(x^2+x-7) in(0,5)#?
  
• Integrate 2sinx+3cosx/3sinx+4cosx??
  
• How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=(2x)/(x^2-1)#?
  
• How do you solve?
  
• What is the equation of the tangent line of #r=4cos(-theta+(5pi)/6) +sin(theta)# at #theta=(7pi)/12#?
  
• Sketch #r = cos(theta) + sin(2theta)# and find the total area covered by this graph?
  
• How do you find intercepts, extrema, points of inflections, asymptotes and graph #y=3x^4-6x^2+5/3#?
  
• What is the solution to the equation to find the volume of the solid formed by the lines?
  
• How do you find the equation of the line tangent to #f(x) = (x^3-3x +1)(x+2)# at the point (1, -3)?
  
• What is the final value of this equation?
  
• Equilateral hexagon is revolving around one of its edges. Find the volume of the solid of revolution?
  
• A fence #8 ft# tall runs parallel to a tall building at a distance of #4 ft# 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? (Round your answer to two decimal places)
  
• How do you find the critical points for #f(x) = 2x^(2/3) - 5x^(4/3)# and the local max and min?
  
• How to find the volume by revolving(use disk/washer method)? y=6-2x-x^2, and y=x+6 about the line y=3
  
• What is the equation of the line normal to #f(x)=2 tan(pix -2)# at #x=2#?
  
• How do you find the integral of tanx from #[0,pi/4]# using the simpsons rule using 6 intervals?
  
• Use shell method to find the volume of the solid generated by revolving the region bounded by y=e^x,y=e^-x,and x=1 about x =-1?
  
• What are the local extrema of #f(x)= (x^3-x^2-5x+4)/(x-2)^2#?
  
• A rectangular prism measures 8 inches in width, 12 inches in length, and 4 inches in height. What is the surface area of the prism?
  
• What is the arclength of #f(x)=x^2/(4-x^2)^(1/3) # in the interval #[0,1]#?
  
• How to find the area of triangle whose vertices are #(3,-1),(2,7) and (-5,6)# ?
  
• How to find the fourth derivative of cos(x^2)?
  
• What are the critical values, if any, of #f(x)= x^3 + 20/x^2 + 100/ x^3 + 9x^2 + 15/x - 25 #?
  
• Find the volume of the solid when the y-axis is rotated about the line x = 4 by using cylindrical shells?
  
• What is the surface area produced by rotating #f(x)= xtan2x -tanx , x in [pi/12,(11pi)/12]# around the x-axis?
  
• How do you use the chain rule to differentiate #f(x)=sin(tan(5+1/x)-7x)#?
  
• What are the critical values of #f(x)=1/sqrt(x^2+4)-ln(x^2+4)#?
  
• Evaluate the integral #int2x(ln(x^9))^2dx#?
  
• Evaluate #int_(pi/2)^(pi/4)19xsqrt(1-cos(2x)dx# ?
  
• What are the extrema and saddle points of #f(x, y) = x^2 + y^2 xy+27/x+27/y#?
  
• What are the critical points of #f(x) =e^x-(xlnx)/(x-2)^2#?
  
• What is the solution of the following system?:# 9x + 9y + z = -112, 8x + 5y - 9z = -137, 7x + 4y + 3z = -64#
  
• What is the surface area of the solid created by revolving #f(x)=(x-3/2)^2# for #x in [1,2]# around the x-axis?
  
• How do you find the critical numbers for #(2-x)/(x+2)^3# to determine the maximum and minimum?
  
• How do you find the equation of a line tangent to the function #y=x^2(x-2)^3# at x=1?
  
• How do you differentiate #y=marctanm#?
  
• What are the local extrema, if any, of #f (x) =x^3+3x^2-5x#?
  
• How do you differentiate #f(x)=ln(sinx)^2/(x^2ln(cos^2x^2))# using the chain rule?
  
• What is the surface area of the solid created by revolving #f(x) = e^(2x) , x in [2,7]# around the x axis?
  
• Evaluate the integral of (x√x-√3dx using substitution method?
  
• What are the critical values, if any, of #f(x)=(e^(x^2)+6e^x)/(x^2-x)#?
  
• #int e^(-i0.2t)dt#?
  
• Question. Compute the arc length of the graph #f(x)=x^(3/2)# over #[0,1]#?
  
• How do you integrate #(x^2 + 3x +1)/(x^2 - x - 6)#?
  
• How do you find the definite integral for: #sqrt(4+3(t^4))dt # for the intervals #[1, 4]#?
  
• What is #int_1^ln5 xe^(x^2)+x^2e^x+x^3+e^(x^3) dx#?
  
• How do you integrate #( x-2 ) / (x^2 + 4x + 3)# using partial fractions?
  
• How do you find the volume bounded by #y = 2x^2#, #y = 2x –3#, x + 1 = 0 and x = 2 revolved about the x=4?
  
• Help me ,Integral of the trigonometric functions:? #int_0^(pi/2)sin^4x*cos^2xdx#
  
• What is the integral of #int (3x+1) / (2x^2 -6x +5))dx#?
  
• What are extrema and saddle points of #f(x, y) = x^3y + 36x^2 - 8y#?
  
• Ann, Kevin, and Goran sent a total of 101 text messages during the weekend. Kevin sent 6 more messages than Ann. Goran sent 3 times as many messages as Ann. How many messages did they each send?
  
• How to investigate the following function and plot its graph using the methods of differential calculus: y=e^[1/2(x+1)] / x+1 ?
  
• How do you find the volume of the solid generated by revolving the bounded region by the graphs of #y=-x+2#, #y=0#, #x=0# about the y-axis?
  
• How do you find the indefinite integral of ∫e^3√x dx?
  
• How to investigate the following function and plot its graphs using the methods of differential calculus? y=3x-2 / x^2
  
• What is the surface area produced by rotating #f(x)=1/x-1/(x+3), x in [1,3]# around the x-axis?
  
• How do you find local maximum value of f using the first and second derivative tests: #1/3(y-2)=sin1/2(x-90*) #?
  
• If f(x)=3x^1/3 -4x+1, find the maximum and minimum of f on [-1,8]?
  
• Calculate the air of the area bounded by the curve #y=-sqrt(x+16)+2#, the axis of #x#, the axix of #y# the and the line #x=15#. ?
  
• How do you find the indefinite integral of ∫ x^2 - 2 dx / x^3 - 4x ?
  
• How do you find the indefinite integral of ∫ (7x-1) dx / √( 3x^2 - 6x + 4 ) ?
  
• How do I find the area between y=x^3 and it’s tangent at x=1 ?
  
• How do I find the length of y=1/2 (e^x + e^-x) from the x=0 and x=b ?
  
• How do you find the volume of the solid formed by revolving the region bounded by the graphs of the equations #y=2x#, #y=4#, #x=0# using the shell method?
  
• How do you find a definite integral that represents the arc length of the curve over the indicated interval #y=x^2+x+4# for #0lexle2# ?
  
• How do you find the area of the surface generated by revolving the curve #y=x^3/3# on the interval [0,3], about the x-axis?
  
• Sketch the region bounded by the graphs of the algebraic functions and find the area of the region f (y) = 1 - y^2 and g (y) = y - 1 ?
  
• How do I find the length of the specified arc of the given curve? y^2=x^3 between (0,0) and (4,8)
  
• Sketch the region bounded by the graphs of the algebraic functions and find the area of the region. f (x) = -x^2 + 2x + 3 and g (x) = x + 1 ?
  
• How do you integrate #int sqrt(-x^2-6x+16)/xdx# using trigonometric substitution?
  
• How to integrate ∫ (x^2−9)^(3/2) dx?
  
• What is the slope of the line normal to the tangent line of #f(x) = xcotx+2xsin(x-pi/3) # at # x= (5pi)/8 #?
  
• How do you find the derivative of #y=x(arcsin)(x^2)#?
  
• Differentiate?
  
• Integrating with respect to y, Skecth the following regions (if a figure is not given) and find the area? how to solve this problem step by step with application of integration?
  
• What is the surface area produced by rotating #f(x)=3x^3+6x^2-2x+3, x in [-3,2]# around the x-axis?
  
• What are the critical values of #f(x)=xe^(2x+5)-x^3e^(-x^2-x)#?
  
• The area enclosed by the curves y=-(x-1)^2+5, y=x^2, and the y-axis is rotated about the line x=4 to form a solid. What is the volume of the solid?
  
• Let R be the region in the first quadrant enclosed by the graphs of #y=e^(-x^2)#, #y=1-cosx#, and the y axis, how do you find the volume of the solid generated when the region R is revolved about the x axis?
  
• How do you find critical point for this equation #f(x,y)=6x^7+7y^2+8xy+9#?
  
• Find the derivative of the function?
  
• How do you integrate #int x^3/sqrt(4x^2+8x+50) dx# using trigonometric substitution?
  
• How do you use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by #y=x^6# and #y=sin((pix)/2)# is rotated about the line x=-4?
  
• Use the method of cylindrical shells to find the volume generated y rotating the region bounded by the given curves about the x-axis?
  
• What is #int (2x^3-3x^2-2x-3 ) / (-8x^2+ 2 x -2 )#?
  
• What are the critical values, if any, of # f(x)= 4 x ^ (5/4 ) - 8 x ^ (1/4)#?
  
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