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I can answer questions from the standard four semester Calculus sequence. I am not prepared for questions on Tensor Calculus. Everything else is welcome. Derivatives, partial derivatives, ordinary differential equations, single and multiple integrals, change of variable, vector integration (Green`s Theorem, Stokes, and Gauss) and applications.

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Ph.D. in Mathematics and many years teaching Calculus at state universities.


B.S. , M.S. , Ph.D.

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Recent Answers from Socrates

2016-01-13 Calculus Optimization:

Let l be the length and w be the width of the pasture. The area is wl . There are 2l + 3w meters of fencing used , so 400 = 2l + 3w .Then l= 200 - (3/2)w    So the area is wl = (w)(200 - (3/2)w) =   200w

2015-12-14 Optimization Calculus:

Let t be the number of trees planted.  The number of oranges per tree will be  400 - 20 (t - 16) =    720 - 20t      So the total yield will be     y  = (t)(720-20t)    y = 720t - 20t^2    y' = 720 - 40t

2015-12-07 Absolute extrema problem:

The absolute maximum occurs where the derivative is 0 or at one of the endpoints .  You found the derivative correctly. Set it equal to zero.   0 = 1-1/x^2  1/x^2 = 1  x^2 = 1  So x=1 is the only value

2015-11-04 Calculus:

Let the radius of the cylinder be r and the height be h.  Volume of the cylinder is πhr^2  Volume of the two hemispheres is (4/3)πr^3  So the volume of the solid is   6 = πhr^2 + (4/3)π

2015-08-28 calculus:

Revenue from selling x items :    R(x) = (x)(200-.01x)      Total cost of making x items :    C(x) = 50x + 20,000      Profit from selling x items is revenue minus cost    P(x) = 200x - .01x^2 - 50x -


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