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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?
- Big O: 2 Functions Map from N to N+ [6/25/1996]
If f, g: N -> N+, then either f(x) is O(g(x)) or g(x) is O(f(x)). Why?
- Brackets or Parentheses? [01/07/1997]
When using interval notation to describe when a function is increasing
and decreasing, how do I know whether to use brackets or parentheses?
- A Brief Overview of Calculus [01/16/2001]
I am required to take a calculus course, but I have no experience with
it. What should I concentrate on?
- Calculate the Derivative for Sqrt(x^5) [03/09/2003]
Why does the calculator fail when I calculate the derivative for
- Calculating Any Root [10/13/1997]
I need to find an algorithm to determine any root of a number. I was told
I could determine the estimated value by using Newton's Method...
- Calculating the Shortest Flight Path [10/30/1997]
Is this spherical trigonometry or can it be solved using simpler
- Calculus (Area of a Plane Region) [5/20/1996]
Problem: y = 4-x2 ; x axis - a) Draw a figure showing the region and a
rectangular element of area; b) express the area of the region as the
limit of a Riemann sum; c) find the limit in part b by evaluating a
definite integral by the second fundamental theorem of the calculus.
- Calculus Constants [11/16/1994]
If a "u substitution" is made for different parts of the function, I get
different answers. However the back of my book says that only one of the
answers is correct. Here is the problem: Integral of secant squared of 3x
times tangent of 3x.
- Calculus - limits [12/10/1995]
Find all the discontinuities of the following function and label those
that are removable...
- Calculus: Limits [11/24/1997]
Why does my textbook define the limit of (1/x) as x approaches zero as
- Calculus (Minimizing Volume) [5/13/1996]
The arch y=sin x,0 less than or = to x less than or = to pi, is revolved
around the line y=c to generate a solid. Find the value of c that
minimizes the volume.
- Calculus of Piecewise Functions [06/07/2003]
Can I take the integral or derivative of a piecewise function like the
floor function [u] or the absolute value function |u| and still notate
it in concise form, |U| or [U]?
- Calculus Problem Using Taylor Series [2/16/1996]
Looking at the equation: 1 + x*2^(x-1)
- A Calculus Question [02/09/1998]
I figured this worked out to -1/2: lim (x - (x^2 + x)^(1/2)) (x going to
- Calculus Questions [1/27/1995]
A student from Riverdale has interesting integration questions.
- Calculus: Rate of Change in Volume [07/27/1997]
The radius of a right circular cylinder is decreasing at the rate of 4
feet per minute, while the height is increasing at the rate of 2 feet per
minute. Find the rate of change in the volume when the radius is 2 feet
and the height is 6 feet.
- Calculus - Shell or Washer Method? [08/23/1997]
I have a question regarding how to set up integrals for the volume of
- Calculus Starting Points [10/23/2001]
I want to learn calculus because I have heard that it is important for
applied math in engineering and I want to be an engineer. What should I
learn, and in what order?
- Calculus Word Problems [04/03/1997]
Minimizing functions and costs.
- Can dy/dx Be Treated as a Fraction? [08/26/2004]
I learned that dy/dx was a notation that implied 'derivative of y with
respect to x.' But in some calculus work, dy and dx seem to have
individual meanings and dy/dx is treated as a fraction. How is this
- Can f'(-1) Equal Zero and f''(-1) Not Equal Zero? [03/23/2004]
Is it possible to have a derivative of zero and then have a double
derivative that is not zero at that same x value? How?
- Carbon Dating the Shroud of Turin [05/16/2000]
In 1988, scientists found that the Shroud of Turin contained 91% of the
amount of carbon-14 contained in freshly made cloth of the same material.
How old is the Shroud according to the data?
- Cardan's Cubic Method [7/19/1996]
Cardan's well known formula solution of cubic equation x^3 - 3x^2 -
x - Sqrt = 0 gives us a single "monstrous" algebraic real root
which appears to defy further simplification....
- Cases Where the Newton-Raphson Method Fails [06/30/2005]
Why does the Newton-Raphson method work for some functions but not for
- Catenary Curve [03/30/1999]
Find the vertex of a catenary curve.
- Cauchy Principal Value Integral [09/17/2002]
Why isn't an integral from negative infinity to positive infinity
defined as the limit as t (or any other variable) approaches infinity
of the integral from -t to t?
- Center of Mass [02/22/1999]
Find the center of mass of a thin plate of constant density covering the
region bounded by the parabolas y = 2x^2-4x and y = 2x-x^2.
- Center of Mass of a Semicircle [06/14/1999]
Is there a standard formula I can use to know where the center of mass of
a semicircle is?
- Centroid of an Arc [03/20/2002]
How do I find the centroid (or centre of gravity) of an arc of a circle?
- Chain Rule [10/23/1996]
I have a question on the "chain rule" when finding the derivatives of
- Chain Rule and Product Rule: Differentiating [02/19/1998]
Why isn't the result what I expect when I use the Chain Rule and the
Product Rule to differentiate?
- Chain Rule Applied to Exponential Functions [10/11/2004]
How do I use the Chain Rule to find the derivative of a function such
as f(t) = 27 e^(-.14t)?
- Chain Rule: Function Notation [9/5/1996]
How can I apply the chain rule to find du/dx for dy/dx=(nu^n-1)*(du/dx)?
- Chain Rule Notation [04/21/1999]
Taking the derivative of a function of a function.
- Chain Rule: Prove the Quotient [05/30/2001]
Prove the quotient where u/v is uv^-1 using the product rule and the
chain rule for (dv^-1/dx...
- Changing Angle of a Tank [06/11/2003]
Points A and B represent pressure sensors in fixed positions on the
base of a round tank. The chord through CD represents the water level
in the tank. Lines a and b are the heights of water registered by each
- Choosing Factors When Integrating by Parts [10/08/2003]
When integrating by parts, how do I decide what factors to use?
- Classifying Cubics into Three Basic Types [08/11/2002]
How can I classify each of y=x^3+x^2, y=x^3-2x^2, y=x^3-2x^2+x, y=x^3-
2x^2+2x, and y=-x^3+x^2-x into one of three basic types without
actually drawing their graphs?
- Cola Consumption [05/03/1999]
The rate of consumption of Cola in the U.S. is S(t)= Ce^kt where S is
measured in billions of gallons per year and t is measured in years from
the beginning of 1980...
- Computing e^(-2) Using a Power Series [04/16/2005]
Use a power series to compute e^(-2) to four decimal place accuracy.
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