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Browse High School Calculus
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
Chain rule.
Maximizing the volume of a box.
Maximizing the volume of a cylinder.
Volume of a tank.
What is a derivative?
 Minimizing the Cost of Phone Line Construction [12/3/1995]

A telephone company has to run a line from point A on one side of a river
to another point B that is on the other side, 5km down from the point
opposite A. The river is uniformly 12km wide. The company can run the
line along the shoreline to a point C and then under the river to B. The
cost of the line along the shore is $1000 per km and the cost under the
river is twice as much. Where should point C be to minimize the cost?
 Minimizing the Length of a Crease [11/11/1999]

How can I minimize the the length (L) of the crease if one of the corners
of an 8.5" x 11" sheet of paper is lifted up and placed on the opposite
longer edge, and then the paper is smoothed flat?
 Minimizing the Sums of Squares [06/12/1998]

Find two numbers such that their sum is 20, and the sum of their squares
is as small as possible.
 Minimizing the Surface Area of a Can [05/22/2000]

What coke can dimensions would use the least amount of aluminum while
still holding 375 ml?
 Minimizing the Time to Rescue [11/29/1999]

A man is drowning in the water 300 meters down the beach and 100 meters
out from where I'm standing. I can run 5 meters/second and swim 3
meters/second...
 Minimum and Maximum Pollution [04/26/2000]

Find the points of minimum and maximum pollution between two plants
releasing 60 and 240 ppm of pollution...
 Minimum, Maximum Value of a Twovariable Function [6/27/1996]

Find f min and f max where x and y are real numbers and f(x,y) = 2(sin
x)(cos y)+3(sin x)(siny)+6(cos x).
 Minimum Value Problem [7/14/1995]

I need to find the minimum value of E for E = be^(ar)  dr^(6) where b,
a, and d are constants and r is the variable.
 Min, Max of 3Variable Function [8/16/1996]

Find all the critical points and determine their nature for the function
z = x^3  6xy + y^3.
 Modelling Discrete Data with Exponential Functions [5/14/1996]

How can I fit an exponential function to a set of three discrete data
points?
 Monkey Climbing a Chain [09/22/1999]

A 20lb. monkey is attached to a 50ft. chain that weighs 0.5 lb. per
(linear) foot...
 The Monotone Convergence Theorem [10/02/1998]

Could you please explain the meaning and purpose of the monotone
convergence theorem?
 Moving a Circle on a Polar Graph [05/04/2001]

How do you move a circle so the center is not (0,0), but to where the
center can be (r,[theta])?
 Moving Particle [07/14/1999]

Assume a particle moves on the xaxis according to the formula x = t^ 3
6t^2+9t+5. Find: the velocity when t = 3...
 The Moving Shadow [03/24/1999]

A man walks toward a light... at what rate does the tip of his shadow
move and at what rate does its length change?
 Multidimensional Calculus and Vector Geometry [02/09/1999]

The depth of iron ore can be approximated by a plane...
 Navigation Formula [10/14/1996]

Given the starting latitude, longitude, distance, and course of a plane,
what formula gives its destination latitude and longitude?
 NewtonRaphson Method [02/28/2000]

How can I find the 1st, 2nd, 3rd iterations and the parameters of x^3 
13.1x^2 + 48.48x  46.62 using the NewtonRaphson method?
 NewtonRaphson Method [06/24/2009]

Are there any equations that cannot be solved using the NewtonRaphson
method, regardless of the initial estimate?
 Newton's Method and Square Roots [12/04/1998]

Can you explain how finding square roots by hand relates to Newton's
method for approximating the zero of a function?
 NonConstant Functions [02/12/2001]

Are there any nonconstant functions f and g such that (f*g)' = f'*g'?
 Nondifferentiable Functions [11/6/1994]

In my calculus book, it mentions a function that is not differentiable
at any point due to the fact that it is not smooth at any point. It does
not go any farther, and I was interested in hearing more.
 NonLinear Equation [2/13/1996]

Solve 5x^2 + log(x) = 0 for x...
 Nonvertical Asymptotes [10/16/2001]

Does this problem have slant asymptotes? f(x)=(x^(4/3)+x^(1/3)2)/(x^
(4/3)16). I'm also having trouble taking the derivative of this problem:
f(x)=((x^2(x+1))(1x))^(1/2).
 A Norman Window [1/16/1995]

A Norman window is a window in the shape of a rectangle with a semicircle
attached to the top. Assuming that the perimeter of the window is 12
feet, find the dimensions that allow the maximum amount of light to
enter.
 The N Targets Problem [11/15/2001]

Given n targets with equal probability of being hit by a cannon, that is,
1/n. Let X be the number of firings required to hit all the targets. What
is the expectation E(X) of X?
 Numeric Derivatives Using TI83, TI92 [10/17/2003]

My calculator says that the numeric derivative of sin(x) is
sin(2x)/(2x). Shouldn't it be cos(x)?
 Oblique Asymptotes [04/03/2002]

I'm stuck on how to calculate oblique limits, for example, x^2/(x3).
 Odd Bernoulli Numbers Must Be 0 [02/16/2003]

Take the second derivative of t/exp(t) 1 and find that it is an even
function; show that an even function, when expressed as a Taylor
Series, has only even powers of t; draw the conclusion that the odd
Bernoulli numbers have to be 0.
 ODEs and Integration with the Chain Rule [05/30/1998]

What is an ordinary differential equation? How do you integrate f'(x) =
(x1)^4?
 Oil Can Dimensions [12/11/2001]

What are the dimensions of an oil can with a oneliter capacity that uses
the least amount of tin?
 Operating a Tour Service [5/21/1996]

How many people does it take to maximize your profit?
 Optimization [12/13/1995]

An AP Calculus student asks questions about his chapter test.
 Optimization [11/26/1996]

To make a funnel, we take a circular piece of metal, cut out a sector,
and connect the two radial edges together to make an open cone. What
should the angle of the sector be to maximize the volume of the cone?
 Optimization: Minimum Area [11/07/1997]

How do you fold a piece of paper (rect. with width a and unlimited
length) so one corner just reaches the righthand side for minimum area?
 Optimization (MinMax) [01/21/2001]

If a piece of string of fixed length is made to enclose a rectangle, show
that the enclosed area is greatest when the rectangle is a square.
 Optimizing Advertising [10/15/2003]

Doubling the amount spent on advertising increases total income by 20
percent. What is the optimum level of advertising?
 An Ordinary Differential Equation in Everyday Life? [03/26/2011]

A student wonders about the real world applicability of ordinary differential equations.
Doctor Jordan steps through an example.
 Ordinary Differential Equation, Second Order [10/26/2002]

I've been looking for solutions to the differential equation y'' = x^2
/ y^2.
 Parametric Equations [07/21/1998]

A curve is given parametrically by the equations: x = (32k)^2 and y
= (2+k)^2. Find dy/dx, the xintercept, the cartesian equation...
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