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 TOPICS This page:   calculus    Search   Dr. Math See also the Internet Library:   calculus HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry 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? 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 (1-cos 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 real-life 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; x-1 for 14 for function (3x-4). To see if this function exists, you have to check it on both sides. Would you plug in 3 for the left and for the right? Finding the Maximum Area of a Rectangle [1/28/1996] A rectangle is inscribed in a triangle (with certain dimensions). Find the maximum area of the rectangle. Finding the Roots of a Function [11/4/1996] How do you find the positive roots of x^9+3x^8-5x^3+4x+6=0? Show that x^n- 1=0 has exactly 2 roots if n is even, and only 1 real root if n is odd Page: []

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