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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?
 Best Fit Quadratic Curve [02/21/2002]

Given a scatter plot of X and Y cordinates, find the bestfitting
quadratic curve.
 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
sqrt(x^5)?
 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
geometric equations?
 Calculus (Area of a Plane Region) [5/20/1996]

Problem: y = 4x2 ; 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
infinity?
 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^(x1)
 A Calculus Question [02/09/1998]

I figured this worked out to 1/2: lim (x  (x^2 + x)^(1/2)) (x going to
infinity).
 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
revolution.
 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
possible?
 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 carbon14 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[2] = 0 gives us a single "monstrous" algebraic real root
which appears to defy further simplification....
 Cases Where the NewtonRaphson Method Fails [06/30/2005]

Why does the NewtonRaphson method work for some functions but not for
others?
 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^24x and y = 2xx^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
polynomials.
 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^n1)*(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
sensor...
 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^32x^2, y=x^32x^2+x, y=x^3
2x^2+2x, and y=x^3+x^2x 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...
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