Questions asked by Moose21

• Back to user's profile
• Why is (1-x)^(-1/x)=e? I know that (1+x)^(1/x) is equal to e but I don’t understand with the negative there.
  
• How do you solve #lim_x->pi/4 (tanx-cotx)/(x-pi/4)# ?
  
• What is the horizontal asymptote of y=#3e^(-1/x)# ?
  
• If #f(x)=g(x^6)/x^2# , and if g is a differentiable function, find an expression for #f''(x)# ?
  
• Find #(dx/dy)_(x=1)# if #y=u^2-u^3+2u^4# and #u=x/(2x-1)# ?
  
• What does derivative of y with respect to x mean?
  
• Find the derivative of the expression for an unspecified differentiable f(x)?
  
• How do I use one sided derivatives to show that the function #f(x)=x^3 , x<=1# #f(x)=3x , x>1# is not differentiable at x=1?
  
• What would happen to the message if an error were made in transcribing DNA?
  
• A sector of arc length x cm is removed from a circular piece of paper of radius 4 cm. The remaining piece is used to make a cone. Find x so that the volume of the cone is a maximum?
  
• A soda can is to hold 12 fluid ounces. Find the dimensions that will minimize the amount of material used in its construction, assuming the thickness of the material is uniform?
  
• A gutter is to be made using a 5m long rectangular piece of metal that has to be bent to form the open topper gutter. the cross section of the gutter is an isosceles trapezoid with sides making angles 120 degrees with the base?
  
• How do I derive #y=sqrt(9+x^2)+sqrt(x^2-10x+41)#?
  
• A 3m ladder has a bent rung 2m from its base. How fast is the distance the bent rung is from the wall changing when the base of the ladder is 1.7m from the wall and the top of the ladder is sliding down the wall 1m/s?
  
• A corridor of width #a# meets a corridor of width #b# at right angles. Workmen wish to push a heavy beam on dollies around the corner, but they want to be sure it will be able to make the turn before starting. How long a beam will go around the corner ?
  
• Find the volume of the cone of maximum value that can be inscribed in a sphere of radius R?
  
• Find the point on the curve y=cosx closest to the point (0,0)?
  
• How do you solve for x in 2x=sin(2x) ?
  
• The hands on a clock are of length 15mm (minute hand) and 12mm (hour hand). How fast is the distance between the tips of the hands changing at 3:00?
  
• An object starts at rest and moves along a horizontal path. It’s position, s, in meters, is given by #s(t)=t^3-9t^2+24t+5#. Is the object moving away or towards the origin when t=3s?
  
• How to do integrate #int(5x^3-x^2)/(x^2-1)dx# ?
  
• How do you evaluate #int e^(6x)sin(e^(2x))dx# using substitution and and tabular integration?
  
• How do you solve #intx^2/(sqrt(x^2-9))dx# using trig substitution?
  
• How do you solve #intxsqrt(x^2+8)*dx# using trig substitution?
  
• How do you evaluate #int tan^5(theta/2) d(theta)#?
  
• How do you evaluate #int cot^5(2x) dx#?
  
• Find the sum of the vectors u and v it theta is the angle between them?
  
• If #hat a# and #hat b# are unit vectors that make an angle of 60 degrees with each other, calculate?
  
• If #bar u#, #bar v#, and #bar w# are linearly independent vectors, find the values of #t#?