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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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Slope of the Tangent [1/9/1995]

Given y = A sinx + B tanx. Find A and B if the slope of the tangent to the curve at x1 = pi/4 is m1 = 4 + root 2, and at x = 0, m2 = 4.

Snail! [06/20/2002]

A snail is climbing a window-pane, beginning in the evening at a height of e minus 1 meter from the base. It loses 1 meter each night. On the second day, it doubles its altitude of the morning. On the third day, it triples the altitude of the morning, and so on. What will be its altitude on the 51st day at dawn?

Solve It Numerically [05/21/1997]

How do you solve the equation x^x = 100?

Solving a Differential Equation [6/5/1996]

The integral looking somewhat like this: S ((e^u)/u) du has resisted every attack on my part.

Solving a Logarithm [6/29/1996]

log a = -1.3

Solving an Equation using Power Series [05/18/1999]

How does one solve the differential equation (t^4)*x'' + x = 0 for x?

Solving an Equation with Infinite Exponents [03/15/2007]

If x^x^x^x^x^x^x^x^x^x^x...... = 2, solve for x. How can I solve that equation?

Solving a Window Problem with Calculus [11/11/1995]

My question is just like the Norman window question, but I have an isosceles triangle on top. Where do I start? I seem to have 3 unknowns. b, h and x.

Solving Differential Equations [5/8/1996]

(2x^2 + 2y^2 - y)dx + (x^2y + y^3 + x)dy = 0

Solving Equations Numerically: Newton's Method, Bisection Method [11/05/2002]

Can you tell me methods to work out equations that can only be solved numerically and not algebraically, and suggest some good equations with which I could try out these methods on using graphs?

Solving for Arc Length [9/10/1996]

How do I use the formula for arc length solve for the length of the curve?

Solving for Rate [8/8/1996]

In the equation P=V*R/(1-(1+R)^(-n)), how do you solve for "R"?

Solving Functional Equations [08/11/2005]

How can I solve an equation like f(f(x)) + 5f(x) + 7 = x^2 + 6x?

The Speed of Change of a Shadow [12/12/1995]

A street lamp whose light is 5 meters from the ground is 6 meters from a vertical brick wall. A person, 2 meters tall...

A Sphere's Surface Area and Volume [12/17/1998]

What is the relation between a sphere's surface area and its volume? How does their ratio change?

Sphere Surface Area Precision [04/22/2003]

How can the formula 4*pi*r^2 for the surface area of a sphere be precise?

Spread of a Virus Through a City [05/09/2002]

A Flu-like virus is spreading through a city of population 260000 at a rate proportional to the product of the number of people already infected and the number of people stilll uninfected.

Square Roots and Limits [03/12/2003]

Given a value of x, find the value of the expression sqrt(x sqrt(x sqrt(x...

The Squeeze Theorem [10/12/1998]

How do you use the Squeeze Theorem to find the limit of f(x) = x * sin(1/x) as x approaches 0?

Standard vs. Symmetric Derivative of Sin(x) [02/07/2006]

Can I find the derivative of f(x) = sin(x) by using the limit (sin(x+h) - sin(x-h))/2h as h->0 and then using a trig identity to simplify the difference of sines?

Stationary Point [10/27/1999]

How can I show that the curve y = x*ln(2x-3) has no stationary point in the region x greater than 2?

Stokes-Greens-Gauss Theorems [03/25/1997]

Are the Stokes-Greens-Gauss) theorems related? What is their significance?

Strongest Possible Beam From a Log [07/11/2002]

Find the dimensions of the strongest beam that can be cut from a cylindrical log of radius 'a'.

Subdividing a Field; Falling Water Level [7/28/1996]

What's the maximum area I can fence with a thousand yards? A water tank has a shape of a right circular cone... how fast is the water level falling?

Substituting to Simplify the Integral [08/04/2003]

What is the integral of tan^3 x * secx dx?

Substitution [06/18/1997]

Integrate sqrt(x^3-1)/x dx.

Summation Formulas for Trigonometric Functions [04/24/2001]

How do you find the area under the curve of a trigonometric function using the definition of a limit and not an approximation? Are there summation formulas for trigonometric functions?

Surface Area and Volume Derivative [10/30/2000]

For what 3D figures is the derivative of the volume formula equal to the formula for surface area? With respect to which variable would you need to differentiate?

Surface Area and Volume: Related Rates [02/22/1999]

The surface area of a cube is changing at a rate of 8 in./s^2. How fast is the volume changing when the surface area is 60 square inches?

Surface Area of a Football [02/12/1999]

Calculate the surface area of a football with a circumference of 22 inches and an arc length of 14 inches.

Surface Area of an n-dimensional Sphere [07/28/1997]

I was wondering how to calculate the surface area of a sphere in n dimensions.

The Surface Area of a Rotational Curve [04/17/1998]

I'm having difficulty understanding how my math professor proved the formula for the surface area of this curve...

Surface Area of a Sphere [10/03/1997]

How is the surface area of a sphere calculated, and why?

Surface Area of a Sphere [04/10/1998]

Can you derive the formula for the surface area of a sphere?

Taking the Partial Derivative of a Function [09/06/2002]

Are the left and right sides of an equation always symmetric?

Tangents to a Curve That Pass through a Fixed Point [08/08/2008]

How many tangent lines to the curve y = x/(x+1) pass through the point (1,2)? At which points do those tangent lines touch the curve?

Tangents to a Parabola [10/21/1996]

Find the slopes of two lines tangent to the parabola y = x^2 that pass through the point (2,1).

Tangent without a Calculator [06/24/2001]

How do I find a tangent value if I have only an angle, and can't use a calculator?

Tan pi/8 [03/16/2002]

I must find the exact value of tan pi/8.

Taylor approximation of tan^2(x) [6/12/1996]

Just to check that I can't do this because f'(0) = infinity...

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