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Selected answers to common questions:
Maximizing the volume of a box.
Maximizing the volume of a cylinder.
Volume of a tank.
What is a derivative?
- Solving a Window Problem with Calculus [11/11/1995]
My question is just like the Norman window question, but I have an
isosceles triangle on top. Where do I start? I seem to have 3 unknowns.
b, h and x.
- Solving Differential Equations [5/8/1996]
(2x^2 + 2y^2 - y)dx + (x^2y + y^3 + x)dy = 0
- Solving Equations Numerically: Newton's Method, Bisection Method [11/05/2002]
Can you tell me methods to work out equations that can only be solved
numerically and not algebraically, and suggest some good equations
with which I could try out these methods on using graphs?
- Solving for Arc Length [9/10/1996]
How do I use the formula for arc length solve for the length of the
- Solving for Rate [8/8/1996]
In the equation P=V*R/(1-(1+R)^(-n)), how do you solve for "R"?
- Solving Functional Equations [08/11/2005]
How can I solve an equation like f(f(x)) + 5f(x) + 7 = x^2 + 6x?
- The Speed of Change of a Shadow [12/12/1995]
A street lamp whose light is 5 meters from the ground is 6 meters from a
vertical brick wall. A person, 2 meters tall...
- A Sphere's Surface Area and Volume [12/17/1998]
What is the relation between a sphere's surface area and its volume? How
does their ratio change?
- Sphere Surface Area Precision [04/22/2003]
How can the formula 4*pi*r^2 for the surface area of a sphere be
- Spread of a Virus Through a City [05/09/2002]
A Flu-like virus is spreading through a city of population 260000 at
a rate proportional to the product of the number of people already
infected and the number of people stilll uninfected.
- Square Roots and Limits [03/12/2003]
Given a value of x, find the value of the expression sqrt(x sqrt(x
- The Squeeze Theorem [10/12/1998]
How do you use the Squeeze Theorem to find the limit of f(x) = x *
sin(1/x) as x approaches 0?
- Standard vs. Symmetric Derivative of Sin(x) [02/07/2006]
Can I find the derivative of f(x) = sin(x) by using the limit
(sin(x+h) - sin(x-h))/2h as h->0 and then using a trig identity to
simplify the difference of sines?
- Stationary Point [10/27/1999]
How can I show that the curve y = x*ln(2x-3) has no stationary point in
the region x greater than 2?
- Stokes-Greens-Gauss Theorems [03/25/1997]
Are the Stokes-Greens-Gauss) theorems related? What is their
- Strongest Possible Beam From a Log [07/11/2002]
Find the dimensions of the strongest beam that can be cut from a
cylindrical log of radius 'a'.
- Subdividing a Field; Falling Water Level [7/28/1996]
What's the maximum area I can fence with a thousand yards? A water tank
has a shape of a right circular cone... how fast is the water level
- Substituting to Simplify the Integral [08/04/2003]
What is the integral of tan^3 x * secx dx?
- Substitution [06/18/1997]
Integrate sqrt(x^3-1)/x dx.
- Summation Formulas for Trigonometric Functions [04/24/2001]
How do you find the area under the curve of a trigonometric function
using the definition of a limit and not an approximation? Are there
summation formulas for trigonometric functions?
- Surface Area and Volume Derivative [10/30/2000]
For what 3D figures is the derivative of the volume formula equal to the
formula for surface area? With respect to which variable would you need
- Surface Area and Volume: Related Rates [02/22/1999]
The surface area of a cube is changing at a rate of 8 in./s^2. How fast
is the volume changing when the surface area is 60 square inches?
- Surface Area of a Football [02/12/1999]
Calculate the surface area of a football with a circumference of 22
inches and an arc length of 14 inches.
- Surface Area of an n-dimensional Sphere [07/28/1997]
I was wondering how to calculate the surface area of a sphere in n
- The Surface Area of a Rotational Curve [04/17/1998]
I'm having difficulty understanding how my math professor proved the
formula for the surface area of this curve...
- Surface Area of a Sphere [10/03/1997]
How is the surface area of a sphere calculated, and why?
- Surface Area of a Sphere [04/10/1998]
Can you derive the formula for the surface area of a sphere?
- Taking the Partial Derivative of a Function [09/06/2002]
Are the left and right sides of an equation always symmetric?
- Tangents to a Curve That Pass through a Fixed Point [08/08/2008]
How many tangent lines to the curve y = x/(x+1) pass through the point
(1,2)? At which points do those tangent lines touch the curve?
- Tangents to a Parabola [10/21/1996]
Find the slopes of two lines tangent to the parabola y = x^2 that pass
through the point (2,1).
- Tangent without a Calculator [06/24/2001]
How do I find a tangent value if I have only an angle, and can't use a
- Tan pi/8 [03/16/2002]
I must find the exact value of tan pi/8.
- Taylor approximation of tan^2(x) [6/12/1996]
Just to check that I can't do this because f'(0) = infinity...
- Taylor Series (Calculus II) [2/14/1996]
I am having difficulty understanding the Taylor Series and Maclauren
- Taylor Series Expansion [11/24/2001]
A distance from A to B is 1000 meters. As one traverses it at 1 meter per
second, the distance is instantaneously and uniformly stretched 1000
additional meters. How long does it take to get from A to B?
- Time and Mean Velocity [01/16/2003]
Why is s = s0 + v0 t + 1/2 a t^2 true?
- Tipped and Partially Filled Frustum [12/14/2003]
A vessel in a plant where I work is the frustum of a cone on its side.
A liquid is contained in this section and pours out the end of the
cone section, therefore the liquid only takes up a certain portion of
the cone's volume. How can I compute the volume of the liquid?
- Triangle Area [05/24/1999]
How do you find the maximum area of a right triangle?
- Trigonometric Functions and Euler's Identity [04/10/1998]
We need to prove three trigonometric functions in various ways.
- Trigonometry and the Chain Rule [12/01/1998]
I need help differentiating expressions such as: y = 2 csc^3(sqrt(x)) and
y = x/2 - (sin (2x))/4. Where does the chain rule fit in?
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