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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?
 Permutation and Combination Equality [07/18/1999]

Prove that (nC0)^2 + (nC1)^2 + (nC2)^2 + ... + (nCn)^2 = (2nCn), where
nCi = n!/((ni)!*i!).
 Picard's Method [08/10/1997]

Can you tell me about Picard's iteration method of solving differential
equations?
 Plane Flying Parametrically [06/28/1999]

How can I find out when a plane, whose position approaching an airport is
described parametrically by P_t = (1000,500,900)+ t[100,50,90], will
be closest to the traffic control center, located at (24,11,13)?
 Point of Inflection [05/17/1997]

The cubic polynomial h(x) = x^3  3bx^2 + 3cx + d has a local maximum and
a local minimum...
 Point on a Parabola [1/9/1995]

How do you find the point on the parabola y = x^2 nearest the point (
3,0)?
 Points of Intersection [08/31/1997]

Estimate all points of intersection of the graphs f(x) = x + sin x and
g(x) = x^3 by using a calculator or computer. How do you know you have
found them all?
 Polar Coordinates [11/4/1996]

Find the polar equation of x^3+y^3=3axy with x+y+a=0 as an asymptote.
 Polar Coordinates for Velocity and Acceleration of a Particle [03/11/1997]

I know that velocity components are dr/dt and rdo/dt and that components
of acceleration are d^2r/dt^2  r(do/dt)^2, etc. I would appreciate any
help at all in understanding how these are generated and/or how to use
them.
 Position Function of a Moving Particle [9/9/1996]

A particle moves on a straight line with a velocity v(t)=sin(w)cos^2w;
f(0)=0; w is constant; find f(t).
 Possible Proof That 1 + 1 Does Not Equal 2 [04/19/2001]

I just want verification... would this proof work?
 Power Series for Sine and Cosine [10/12/2000]

Can you explain, without using calculus, how to get the power series for
sine and cosine?
 Precalculus Function Question [2/8/1996]

Does the function f(x)=3De^(1/x) have a local minimum?
 Primitive function [6/11/1996]

Give a primitive function of (sin x) / (ln (2 + x^2)).
 Projectile Velocity and Vectors [5/7/1996]

If the initial velocity is 834 meter^2/sec at an angle of 60 degrees, and
x is 21,000, at what time, t, is the object at x = 21000 meters?
 Proof by First Principles [11/16/2001]

How can I prove by first principles that the derivative of tan(x) is
sec^2(x)?
 Proof for the Radius of Curvature [08/17/2003]

The equation of a circle of radius R centered at the origin is
x^2+y^2 = R^2. Demonstrate that the radius of curvature is equal to R.
 Proof of a Bounded Series using the Binomial Theorem [6/6/1995]

Prove that (1+1/n)^n is bounded from above.
 Proof of Absolute Value, Division [7/16/1996]

If y does not equal to 0, prove that x / y = x/y.
 Proof of Cosine of 36 Degrees [11/26/2001]

Prove: cosine {(pi)/5} = {1+5^(1/2)}/4.
 Proof of Derivative for Function f(x) = ax^n [01/14/2004]

Is there a way to prove or show why the derivative of ax^n turns out
to be anx^(n1)?
 Proof of Integration by Parts [02/06/2001]

How do you derive the formula for integration by parts?
 Proof of Series ln(1+x) [11/15/2001]

I need to show that the series ln(1+x) equals xx^2/2+x^3/3x^4/4, and so
on, whenever x is between 1 and 1.
 Proof of Stirling's Approximation [03/09/2006]

Can you prove that lim ((e^n)(n!)) / ((n^n)(n)^1/2 = (2pi)^1/2 ?
 Proof of Tangent Double Angle Identity [7/16/1996]

I would like to see the proof of the tangent double angle identity.
 Proof of the Chain Rule [09/06/2004]

I am using the Chain Rule (dy/dx = dy/du * du/dx) in my math class, and
I would like to see it proved, which we don't do in class.
 Proofs of e [03/21/2002]

I found out that the definition of e is: e = lim, as n approaches
infinity (1+1/n)^n. Is there a proof for this or for 1+2(e1/n)?
 Proof that 2 Equals 1 Using Derivatives [05/10/2000]

If d(x^2)/dx = d(x+x+...+x)/dx, then 2x = 1+1+...+1 = x. What is the
error in this "proof"?
 Proof that INT(1/x)dx = lnx [11/08/1996]

How do you integrate (1/x)dx?
 Proving Limits at Infinity Using the Formal Definition [04/11/2004]

We are required to find a limit (informally), then prove that our answer is correct by using the formal definition of limits. I'm not sure I'm on the right track.
 Proving Limits Formally [01/04/1999]

Given a sequence, I can guess what the limit it. How do I actually prove
my guess is the limit?
 Proving That d(e^x)/dx = e^x [06/30/1999]

How can I find the derivative of y = e^x, using the definition of the
derivative?
 Proving the Derivative of e^x Is e^x [02/20/2006]

What is the delta x proof of (dy/dx)e^x = e^x?
 Ptolemy's Theorem and Doubleangle Formulas [7/11/1996]

Is it possible to show the formula Sin(AB), Cos(A+B) or Cos(AB) using
Ptolemy's Theorem?
 Quadratic Extrema [07/20/2002]

Can you tell me how to find the minimum or maximum of a quadratic
function?
 Quadratic Function and Diagonals of a Diamond [6/14/1996]

The sum of the two lozenges (diagonals of a diamond) are maximum when the
angle between the longest lozenge and the side of the diamond is 30
degrees, diamond side length = sqrt 2...
 Quotient Function Mnemonic [03/11/2002]

Help me to differentiate the following: x/((x^2)4).
 Raabe's Theorem [8/23/1996]

Regarding Raabe's result for the convergence of a numerical series of
nonnegative terms  I am looking for is a convergent series having m =
1.
 Radian vs. Degree, Sin Derivatives [10/23/2001]

Why do you get a different answer when you ask your calculator for the
derivative of sinx in degree rather than radian mode?
 Radius of Curvature [07/23/2003]

I have several ellipses whose major and minor diameters I know, but
I have no information about their foci.
 Range of rational functions [12/1/1994]

Given the following rational function: f(x)= (x1)/(x^2+3x1), how do you
find the range? Our book gives the answer of: (neg infinity to 0.12] U
[0.65 to pos infinity).
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