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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?
 Integration Trick [8/13/1996]

If f(x)=1/sin(x), what is the integral of f(x)?
 An Integration with Substitution [06/06/1998]

I'm having trouble with the following integration. Is substitution needed
here?
 Intriguing Limit [04/30/1997]

Why is the following true: lim x > oo (11/x)^x = 1/e?
 Introduction to Line Integrals [02/08/2004]

C is the broken path line that goes from (1,1,2) to (2,0,1) by
following a line parallel to the x axis from (1,1,2) to (2,1,2) then
parallel to the y axis from (2,1,2) to (2,0,2) then parallel to the z
axis from (2,0,2) to (2,0,1). Find int_C [ f(x,y,z)*dx + g(x,y,z)*dy
+ h(x,y,z)*dz ].
 Inverse of a Multivariate Function [05/30/2002]

Let f:NxN > N such that f(x,y) = 2^x(2y + 1)  1 for all natural
numbers x, y. Let the inverse of f, g be given by g:N > NxN. Find the
inverse of the function g.
 Inverting Functions [07/19/2002]

To find the inverse of a function y=f(x), do I interchange the
variables x and y, or do I solve for x in terms of y?
 Is Infinity a Number ... in Inversive Geometry? [01/15/2010]

A reader attempts to demonstrate infinity as concretely measurable in
an inversive geometric construction. Doctor Tom explains analyzes the
argument, weighing the pros and cons of the axioms of nonEuclidean
geometries, and going on to expose an apparent paradox.
 Is pi Squared Rational or Irrational? [01/07/2011]

Doctor Ali provides a proof by contradiction.
 Is the Function Invertible? [09/22/1997]

For the following functions f(x) decide if the function is invertible as a
function from R to R...
 Iterated Limits [5/25/1996]

I don't know how to do the following problems...
 Jerk  Derivative of Acceleration [03/16/2001]

I need a mathematical term that begins with the letter J, its definition,
and a highschoollevel explanation of the term.
 kth Derivative of x^n [03/04/2003]

What is a quick way to find the nth derivative of a function? Example:
the 7th derivative of x^8.
 LaGrange Error for a Taylor Polynomial [05/28/2000]

How can you find the LaGrange error for a Taylor polynomial?
 Lagrange Multipliers [01/08/1998]

I have a problem with Lagrange Multipliers  can you help?
 Lagrange Multipliers [01/28/2001]

The temperature of a point(x,y,z) on the unit sphere is given by
T(x,y,z)=xy+yz. Using Lagrange multipliers, find the temperature of the
hottest point on the sphere.
 Lagrange Multipliers and Constraints [11/24/1998]

When using the Lagrange Multiplier method, how do you determine which of
the two equations is the constraint?
 Laplace Transform [01/25/2001]

What are Laplace transforms, and what are their applications?
 Latus Rectum [08/08/2002]

I'm trying to find the definition, an explanation, a formula, or
anything that will help me to better understand what latus rectum is.
 Learning Differential Equations [7/15/1996]

What resources can I use to learn about differential equations?
 Lengthening Shadow [10/13/2003]

A man 6 feet tall walks at 4 miles an hour directly away from a
lampost 18 feet tall. Why does his shadow lengthen at a constant rate?
 Length of a Cubic Curve [12/10/1997]

I need to calculate the true length of a cubic curve.
 Let f(x) = 1 + 1/2 + 1/3 + ... + 1/[(2^n)1] [05/15/1999]

Which of the following inequalities are correct?
 L'Hopital's Rule [4/23/1995]

I can't figure out how to take the limit using L'Hopital's rule on this
problem...
 L'Hopital's Rule [8/11/1996]

How can I solve the following problem: limit as x> infinity of x^(1/ x)?
 L'Hopital's Rule and Limits [8/7/1995]

Find the limit of [sin 3x / tan (x/3)] as x goes to 0.
 Lifting an Object of Changing Mass [7/28/1996]

Suppose you grab the end of a chain that weights 3 lb/ft and lift it
straight up off the floor at a constant speed of 2 ft/s: determine the
force as a function of height; how much work do you do in lifting the top
of the chain 4 feet?
 Limit As n Approaches Infinity [9/7/1996]

How do I find the limit (n> infin.) of (sqrt(2n^2+1))/(2n1)?
 Limit Intuitions [10/01/1998]

Can you explain the intuition behind the formal definition of a limit?
derive the equation of the tangent line of a function at a given point?
 Limit of a Factorial and Exponent in x [05/21/2014]

A calculus teacher wonders how to prove a limit involving the factorial of a variable raised
to a power of the same unknown. Seeing an opportunity to prove a simple version of Stirling's Approximation, Doctor Vogler introduces it with integral calculus and the Squeeze Theorem.
 Limit of n^2/2^n as n Tends to Infinity [12/05/2002]

Demonstrate that the limit as n tends to infinity of the fraction n^2
/ 2^n = 0.
 The Limit of Sin(1/x) [10/02/1998]

Why does the sine of 1/x have no limit as x approaches 0?
 Limit of x sin(1/x) [04/23/2002]

I assumed from the graph that the function had a limit at x=0 of 0,
but since it involves sin(1/0) I can not prove this using the basic
trigonometric limits (sin x/x and (1cos x)/x), L'Hopital's
rule, or by rearranging the equation. Can you help?
 Limit Problem [7/16/1995]

Find the limit of (x^2 + 2x) / (5x  5) as x tends to infinity.
 A Limit Problem [10/24/1996]

What is the limit of (x^2 4) / (2x) as x approaches infinity?
 Limit Problems [08/08/1998]

What is the limit of (sqrt(2t)  sqrt(2))/t as t>0?
 Limit Proof [7/13/1996]

If lim(An/n) = L and L>0, how do you show that lim(An) = + infinity?
 Limit Proofs with L'Hopital's Rule [05/27/1998]

How would you prove the following three limits? ...
 Limits Approaching Infinity [02/16/2002]

Is the only way to answer them by memorizing all the general questions
you may come across?
 Limits  Indeterminate Forms [10/12/1997]

I cannot do a problem where I need to convert into the form 0/0 and then
use L'Hopital's Rule...
 Limits of MultiVariable Functions [11/12/2004]

Find the limit, if it exists, or show that the limit doesn't exist:
lim (x*y*cos(y))/(3*x^2 + y^2) as (x,y) ==> (0,0).
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