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High School Archive

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?

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Finding the Shape of a Funnel Curve [04/08/2001]

Find the equation of the curve of revolution of a coin leaving a chute.

Finding the Sum of Arithmetico-Geometric Series [09/13/2004]

Find the sum of the infinite series 1/7 + 4/(7^2) + 9/(7^3) + 16/(7^4) + ... I would also like to know if there is a general rule to find the sum of (n^2/p^n) for n = 1 to infinity.

Finding the Width of a Corridor [11/13/1995]

A steel girder 27 ft long is moved horizontally along a passageway 8 ft wide and into a corridor at right angles to the passageway. How wide must the corridor be for the girder to go around the corner? Neglect the horizontal width of the girder.

Finding Volumes: Washer/Disc Methods [01/05/1998]

I am having difficulties in the washer and disc methods of finding volumes, as in the problem y=x^2, x=3 about the y axis.

Find Polynomial G(x) (Impossibility) [7/1/1996]

For all real x, F(x) = x+3 and G(x) is a polynomial of degree two such that G(F(x)) = x+2. Find G(x).

Find the Density Function [01/24/2002]

Suppose X1, X2, X3 are independent and uniform on(0,1). Find the density function of S = X1 + X2 + X3.

Find the Path and the Time Taken [10/17/2001]

A man wants to cross a river 500m wide. His rowing speed relative to the water is 3000 m/hr. The river flows at a speed of 1200 m/hr...

Find x in Degrees, not Radians [01/14/1998]

I need to find the derivative of sin(x) when x is in degrees, not radians.

Fixed-Point Theorem [05/02/2002]

An intuitive reason why the theorem is true, and a proof.

Floor and Mod Functions Discontinuous [10/10/2001]

What is f(x) = x mod b for some fixed b?

Formula for the Curvative of a Curve [10/10/2002]

Is there a formula or theorem I can use to convince someone who believes a wall has only side that there is another side to it?

Formula for the Trapezoid Rule [07/31/1999]

I am writing a program to find the moment area of any shape...

Formula to Sum a Series of Square Roots [07/03/2004]

Is there a way to calculate the sum of the series sqrt(x) as x goes from 1 to n?

Fresnel Integral of sin(x^2) [03/28/2002]

I can not see how this integral from 0 to infinity can have any limit at all. If we used infinite series, we would not get a value for x = infinity.

Frustum of a Pyramid with a Rectangular Base [02/20/2002]

I am an engineer with a water treatment agency and need to figure the amount of water per foot of elevation in our reservoirs...

Fuel Left in an Ellipsoidal Tank [10/19/2002]

How much fuel is left in a tank at any depth, given that the tank is ellipsoidal?

Functions of a Complex Variable [10/05/2002]

Show that w=f(z*), where z*=x-iy and f is a differentiable function, is not an analytic function of z.

Function X is a variable... [1/9/1995]

Right now we are learning general exponential and logarithmic functions. In one of my homework problems....

The Gamma Function and Its Derivative [05/26/1998]

Does n! = the integral from 0 to infinity of (x^n)(e^-x)dx hold true for all real numbers? If so, can we find the derivative of n!?

Gamma Function Division [12/20/2005]

Is there a formula for Gamma(n)/Gamma(m) for n and m having integer values >= 1 and m < n?

Gas in a Cylindrical Tank with Hemispheric Caps [02/09/2010]

Doctor Jeremiah uses calculus to calculate how much gas a large pill- shaped tank holds.

General and Particular Solutions [01/08/1999]

What is the difference between a general solution and a particular solution of a differential equation?

Generalized Cubic Equation [05/22/2000]

How do we find a generalized cubic rule for a family of cubics that cut through the point (1,1), have a gradient of 2 when x = 1, and have 1 stationary point?

General Solution of dy/dt + y = t [10/25/1999]

How can I find the general solution to the equation dy/dt + y = t?

Generating the Volume of an n-Sphere [02/07/2002]

Could you help me find an equation for the integration of a unit-ball in n-dimensions?

Geometric Proof of a Limit [12/06/2003]

Prove that lim[x->0](sinx)/x = 1 without using L'Hopital's rule.

Goat and Silo [05/31/2001]

A goat is roped to a point A next to a silo 30 ft. in diameter. The rope is 15pi feet long. How much area can goat graze?

Goat tied to a barn [11/8/1994]

If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? Assume the goat is tied to a corner.

The Gradient [06/03/1997]

What is the geometrical interpretation of the gradient?

Graphing Absolute Values [07/03/2002]

I have a function, f(x), that I can graph, but I don't understand how to graph |f(x)|.

Graphing Limits [09/12/2001]

I was hoping you could explain the concept of "limits" and how to read them from graphs.

Graphs and Gradients [05/13/2003]

Sketch graphs of f and f' for f(x) = sin x and guess the formula for f'(x).

Great Circle Parametric Equation [05/25/1998]

How can you calculate specific points of a great circle on a sphere? Can you help me find the parametric equation?

Half-Life of a Radioactive Substance [8/4/1995]

The half-life of a radioactive substance is d days. If you begin with a sample weighing b g, how long will it be until c g remains?

Halving and Halving Again - Zeno's Paradox [8/22/1996]

Since we can never really get to zero by reducing something by halves, does that mean that we are floating on air?

Harmonic Series [04/28/2003]

Prove that if in the sum 1 + 1/2 + 1/3 + ... + 1/n we throw out each term that contains 9 as a digit in its denominator, then the sum of the remaining terms is less than 80.

Heat Supplied and Heat Loss of a Furnace [05/17/2000]

Heat is supplied by a furnace at a constant rate, but is lost at a rate determined by the difference between its temperature and the temperature of its surroundings...

Helix Lying on a Cylinder [11/26/1997]

I am trying to find a parametric equation for a helix (in 3 space) lying on the cylinder...

History and Applications of the Natural Logarithm [03/02/1998]

I'm so surprised at how often the number e comes up. Where did it come from? Who first derived it? Why is it so common in the field of biology?

How a Calculator Determines Values of Trig Functions [03/19/2005]

I'm interested in how my calculator finds the answer of sin(pi/4) or tan(pi/6), for example. Does it use power series?

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