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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 best-fitting 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?

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 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 = 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 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^(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 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 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[2] = 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 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^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 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^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 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^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?

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