Answers created by Frederico Guizini S.
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What is the equation of the line that is normal to #f(x)= ln(x^2+1)-2x #at # x= 1 #?
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How do you differentiate #f(x) = (tan(3x-2))/(e^(1-x)-1)# using the quotient rule?
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Question #dedf0
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How do you differentiate #y=(-2x^4+5x^2+4)(-3x^2+2)# using the product rule?
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How do you integrate? dx/sqrt(4x^2-8x-1)
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How do you use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region #y= sqrt x#, #y=0# and #y=(x-3)/2# rotated about the x-axis?
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Find the volume of the solid whose base is the region in the first quadrant bounded by y=x^2 y=x2, y=1, and the y-axis and whose cross-sections perpendicular to the y axis are equilateral triangles.
Volume = ???
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What are the local extrema, if any, of #f (x) =(x^2-2x)^3+(4x^2-3x^4)*e^(2x)#?
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How do i integrate this?
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Question #e882e
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How do you find local min and max for f(x) = −x^4 − x^2?
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How do you find the area of the surface generated by rotating the curve about the x-axis #y=1/4x^4+1/8x^-2, 1<=x<=2#?
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What are the points of inflection of #f(x)= (5x^2 + 4x )/ (x^3 + 5x^2+1)#?
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Using a crankshaft, a carpenter drills a hole, 1 cm in radius, through a wooden ball along a diameter. If the radius of the ball is 4 cm, what is the volume of wood remaining?
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Question #9157d
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A cylindrical jar, of radius 3 cm, contains water to a depth of 5 cm. The water is then poured at a steady rate into an inverted conical container with its axis vertical. ?
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Question #1c2e3
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Question #112c3
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Can someone explain how to do this?
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How do you differentiate #f(x)=[(3x^2 + 1)^(1/3) - 5]^2 / [5x^2 + 4]^(1/2)# using the quotient rule?
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The parametric equations of a curve are x=tan2θ and y=cot2θ.find the equations of the tangent and the normal to the curve at the point where θ=pi/6?
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The equation of two planes are given by: x+2y+z=4 and 2x-4y-z=2.
Find the vector equation of the plane which contains the point (3,0,0) and is perpendicular to the two given planes. ?
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Given that y=cos2x/(1+sin2x)
Show that (d^2y/dx^2)+2y (dy/dx)=0?
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Do you have to integrate to solve this?
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Question #4ed4a
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How do you determine where the function is increasing or decreasing, and determine where relative maxima and minima occur for #f(x) = 3x^4 + 16x^3 + 24x^2 + 32#?
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What is the equation of the tangent line to the polar curve # f(theta)=theta^2costheta-theta+tan(theta/3) # at #theta = pi#?
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What is the equation of the tangent line of #r=cos(theta-pi/4) +sin^2(theta+pi)-theta# at #theta=(-13pi)/4#?
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What is the equation of the line normal to # f(x)=(x-sinx)/tanx# at # x=pi/3#?
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How do you integrate #f(x)=(3x^2-x)/((x^2-52)(x+4)(x-7))# using partial fractions?
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A right circular cylinder is inscribed in a cone with height 6m and radius 3m. How do you find the largest possible volume of such a cylinder?
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Question #4203f
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Question #f78cb
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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^2#, y=2-x x=0 revolved about the y-axis?
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Let R be the region bounded by y=4/(x^3), y=1/2 and x=1. What is R if it revolved around the line y = -2?
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Question #8a1c7
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Question #b91f8
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Question #3db58
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Question #2b336
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Question #24a41
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Question #f3f57
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Question #780d9
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Question #68b62
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Question #a2f31
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Question #5698e
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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?
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Question #188bc
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Question #72a57
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Question #d21b1
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How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=x^2+1, y=-x^2+2x+5, x=0, x=3#, about the x axis?
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The base of a solid is the region in the first quadrant enclosed by the graph of #y= 2-(x^2)# and the coordinate axes. If every cross section of the solid perpendicular to the y-axis is a square, how do you find the volume of the solid?
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Question #a90c1
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How do you find the area of the surface generated by rotating the curve about the x-axis #x=t^2+t, y=2t+1, 0<=t<=1#?
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What is the surface area produced by rotating #f(x)=2/(e^x-3), x in [0,2]# around the x-axis?
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What is the surface area produced by rotating #f(x)=2/x-1/x^2, x in [1,3]# around the x-axis?
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How do you find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line: y= x, #y = sqrt(x)#; about x = 2?
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Question #40f71
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How do you find the volume of a solid that is enclosed by #y=secx#, #x=pi/4#, and the axis revolved about the x axis?
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How do you find the volume of the solid obtained by rotating the region bounded by the curves about the y-axis?
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How do you integrate #int (8x^2 - 11x + 5) / ((2x - 3) (x^2 + 1))# using partial fractions?
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How do you differentiate # (x+y)e^(xy)ln(xy - ysinx) = 2#?
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How do you find the derivative of #y=ln((x+sqrt(1+x^2))/(1+sqrt2))#?
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A rectangle with sides parallel to the axes is inscribed in the region bounded by the axes and the line x+2y = 2. How do you find the maximum area of this triangle?
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Question #56b6c
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How do you integrate #int x^3 sin^2 x dx # using integration by parts?
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What is #int (3sin^2x)/(cos^3(3x)) dx#?
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How do you differentiate # y = 1/4 [ 1/2ln[x^2 -2x +2/ x^2 + 2x +2] + tan^-1[2x/2-x^2]]#?
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What is the arclength of #f(x)=sqrt((x^2-3)(x-1))-3x# on #x in [6,7]#?
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How do you find #(dy)/(dx)# of #tan(x+y+1) = y/sqrt(x+1)# by implicit differentiation?
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How do you differentiate #f(x) = (sqrt(x-5))/(-x^2-2x+1)# using the quotient rule?
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What is the equation of the line normal to # f(x)=-x/ln(2x^3-x)# at # x=1#?
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How do you find the volume bounded by #y=x^2# and the line #y=16# revolved about the y=16?
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How do you integrate #int (8x-1)/(x^3 -1)# using partial fractions?
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What is the area enclosed by #r=5sin(-6theta-(5pi)/8) -2theta# between #theta in [pi/8,(3pi)/4]#?
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What is the area enclosed by #r=-sin(theta+(15pi)/8) -theta# between #theta in [0,(pi)/2]#?
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Question #24492
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What is the equation of the tangent line of #f(x) =sin^3x/x^3-sin(2x)/(2x)# at # x = pi/4#?
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What are the values and types of the critical points, if any, of #f(x) =4x^3+48x^2+26x-246#?
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How do you implicitly differentiate # (xy)^2+xcos(xy)=ln(x/y)+ytan(xy) #?
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How do you differentiate #y=r/sqrt(r^2+1)#?
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What is the slope of the tangent line of #r=theta/3+sin((3theta)/8+(5pi)/3)# at #theta=(11pi)/8#?
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How do you differentiate #f(x)= ( x + 1 )/ ( x - csc x )# using the quotient rule?
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What is the arclength of #f(x)=x^2e^x-xe^(x^2) # in the interval #[0,1]#?
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Question #25ffa
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What is the equation of the tangent line of #f(x)=x/ln(x^2) - x^2/lnx# at #x=3#?
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What is the arclength of the polar curve #f(theta) = -5costheta+sin6theta # over #theta in [0,pi/3] #?
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What is the slope of the line normal to the tangent line of #f(x) = e^(x-3)/x+x^3 # at # x= 2 #?
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If #f(x) =-e^(2x-1) # and #g(x) = -3sec^2x^2 #, what is #f'(g(x)) #?
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How do you find the area in the first quadrant between the graphs of #y^2=(x^3)/3# and #y^2=3x#?
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Question #c1f8f
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Question #6f89a
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The region under the curve #y=sqrt(2x-4)# bounded by #2<=x<=4# 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?
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How do you find the distance travelled from t=0 to #t=2pi# by an object whose motion is #x=cos^2t, y=sin^2t#?
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What is #int arctan(x-1)/arccosx dx#?
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How do you implicitly differentiate #-1=xy^2+2x^2y-e^(3x+7y) #?
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How do you differentiate #y= root3 (5x)^x#?
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What is the arclength of #f(t) = (t-tsqrt(t-1),t/(t^2-1))# on #t in [2,3]#?
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What is the slope of the line normal to the tangent line of #f(x) = 2x-xsqrt(x^2-1) # at # x= 2 #?
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How do you find the volume of the solid generated by revolving the region bounded by the graphs #y=1/x, y=0, x=1, x=4#, about the x axis?
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The region under the curves #1/(x^2+1)=y, 0<=x<=2# is rotated about the x axis. How do you find the volumes of the two solids of revolution?
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