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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?
 An Elliptic Integral [01/05/2003]

Integrate Sqrt[Sin[x]].
 Epsilon/Delta Definition of Limits [08/26/1999]

Can you explain how to use the epsilon/delta definition of limits?
 EpsilonDelta Proofs [09/28/2004]

An explanation of the thinking behind two epsilondelta proofs, one
from a calculus textbook and one from an answer in our archives.
 Equation [04/03/1997]

Solve for x...
 Equation for a Curved Line [01/19/1997]

Is there a formula into which you can enter a starting point, a starting
slope, an ending point, and an ending slope that gives the equation of
the curved line between these points?
 Equation of a Circle [08/25/1997]

Write the equation of the specified circle in general form...
 Equation of Parabola with Given Vertex, Point [8/4/1996]

How do I find the equations for all parabolas containing the origin whose
vertex is at (2,1)?
 Equations for the Paths of Four Lady Bugs [12/02/1998]

Four ladybugs travel from the corners of a square towards the center.
Find the equations that describe the path.
 Escaping L'Hopital's Loop [10/14/2003]

I'm trying to apply L'Hopital's rule, but I keep ending up with 0/0
after each application. What am I missing?
 Euler Equation and DeMoivre's Theorem [05/18/1999]

Do you have a proof of the equation e^(i*Pi) + 1 = 0?
 Evaluate the Limit [12/03/1997]

In Calculus today we were trying to evalulate the limit of (1cos x)/
(x^2) as X>0.
 Evaluating Two Definite Integrals [02/28/1998]

Evaluating a definite integral and determining an enclosed area.
 Exact? Area under a Curve [03/13/1998]

Would you please explain why the area under a curve is exact and not an
approximation?
 Examples of Cooling, Growth and Decay [06/03/1999]

Can you give some real life problems involving Newton's cooling method,
logistic growth, and exponential growth and decay?
 Explaining the Intermediate Value Theorem [02/18/2004]

I want to know how to explain the Intermediate Value Theorem in its
most simple form: If f is a continuous function on the closed interval
[a,b] and N is any number between f(a) and f(b), there must be a
number c in (a,b) such that f(c)= N.
 Explanation of L'Hopital's Rule [02/06/2001]

I understand the method, and I somewhat understand the proof, but can you
give me an explanation of why L'Hopital's Rule actually works?
 Exploring the Distance from (0,0) to (1,1) with Limits [10/15/2006]

Any route traveling from (0,0) to (1,1) going only north and east will
cover a total distance of 2 units. But the straight line distance from
(0,0) to (1,1) is sqrt(2) units. It seems that if I think of a
staircase connecting the two points and let the stairs become
infinitely small, the limit of the north/east route distance should
converge to sqrt(2). But it doesn't! What's going on here?
 Exponential Growth & Compound Interest [6/2/1996]

(1) The cost of goods and services in an urban area increased 1.5% last
month. If the rate continues, what will be the annual rate of increase?
(2) Suppose a certain population increases by 30% every 10 years. By what
percent does it increase each year?
 Exponential Growth of a Population [05/03/1998]

A population P(t) is increasing at a rate directly proportional to 800 
P(t), where the constant of proportionality is k...
 Exponential Growth of Bacteria [8/7/1995]

A colony of N bacteria increases with time according to the formula dN/dT
= kN. If initially there are N' bacteria, show that the number at any
time is given by N = N'e^kt.
 Factoring Polynomials [02/12/1999]

What are some reallife applications of factoring polynomials?
 The Figure of Maximum Area and Given Perimeter [06/02/1998]

Can you help me show, with and without calculus, that the geometric figure of a maximum area and given perimeter is a circle? What are the dimensions of a triangle with perimeter p that encloses the maximum area?
 Find a Function, Integrals [12/17/1997]

Suppose the graph of f has the formula f(x)=x+1 for 0<=x<=1; x1
for 1<x<=2 ...
 Find Curve Given Slope, Point [8/29/1996]

Find the curve whose slope at (x,y) is 3x^2 and which passes through (1,
1).
 Finding a Definite Integral with Natural Log and Sine [05/14/2008]

I'm trying to evaluate the definite integral of ln(sin(x)) dx from 0
to pi. I've tried integration by parts but am not getting anywhere.
 Finding a Limit [02/28/2002]

My calculus teacher gave my class the answer to this limit; however, we
cannot figure out how to get the answer that is given.
 Finding a Vertical Asymptote [05/11/2000]

How can I find the vertical asymptote of the equation xy^2  x^3y = 6?
 Finding First Derivatives by Definition [10/30/1998]

Can you show me an easy example of how to find the first derivative of a
function using the definition?
 Finding Integrals Using Trigonometric Substitutions [10/2/1995]

What is the integral of 1/(x(1x))^(1/2)? How can I integrate this
function using only the derivative of arcsin or arctan?
 Finding Limits Using Natural Logs and L'Hopital's Rule [05/03/1998]

I think I need to use l'Hopital's Rule and the natural logarithm function
to find lim (x goes to 0) [(cos (2x))^(3/(x^2))].
 Finding Maxima and Minima: Turning Points [05/10/1998]

Can you help me find all of the maxima and minima of the function: 5e^(
x/2)sin(2x)?
 Finding Tangents to Curves Using Derivatives [09/29/1999]

Three problems that involve finding the tangents of a curve using
calculus.
 Finding the Area of Overlap between Two Circles [04/16/2008]

Suppose I know the centers and radii of two circles that overlap. How
can I find the area of that overlapping region?
 Finding the Derivative [07/27/1999]

Find dy/dN if y= A*(1  e(cN))* (1  e(cM)).
 Finding the Domain of a Function [9/28/1995]

What is the domain of f(x)=((2x)/(x2))^.5
 Finding the Equation of a Tangent Line [10/6/1995]

What is the equation of the tangent line to the graph of f(x)=x^(2/5) at
the point (32,4)?
 Finding the Equation of a Tangent Line [11/24/1998]

I only have where the tangent intersects the y axis...
 Finding the Extrema of a Function [10/25/1996]

Find the extrema of f(x)=(ln(1+exp(abxcx^2)))/((x+d)^2)...
 Finding the Factorial of NonIntegers [01/06/2005]

I thought the factorial function was only defined for positive
integers, but I notice that my calulator returns a value for
nonintegers like 3.5! What's going on?
 Finding the Indefinite Integral [2/1/1996]

I am trying to find the indefinite integral of the following function:
f(x) = x^x.
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