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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?
- Best Fit Quadratic Curve [02/21/2002]
Given a scatter plot of X and Y cordinates, find the best-fitting
- 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?
- Bound to Confuse [08/07/2017]
An adult wonders about the usefulness of the upper bound and lower bound
theorems. After clarifying their scope, Doctor Peterson delves further into what
conclusions these do allow, and what they do not.
- 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?