The special case of x⁴ - Page 5

Questions
  • 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 to investigate the following function and plot its graphs using the methods of differential calculus? y=3x-2 / x^2
  • 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#. ?
  • Let f(x)=9x^2/4_-5x find f'(x) and f''(x)?
  • How would I take the derivative of #x^2ln(sin4x)#?
  • How do you find the area under the curve #y = 2x - x^2# from x=1 to x=2 with n=4 inscribed rectangles?
  • A curve has parametric equations x=2t-ln2t and y=t²-ln t² where t>0. Find the value of t at the point on the curve where dy/dx =2 . Hence ,find the coordinates of that point?
  • A rectangle has two vertices on the x axis and the other two above the x axis and on the graph of the equation y= 4-x² . Find the dimensions for which the area of such triangle is a maximum ?