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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? Finding the Shape of a Funnel Curve [04/08/2001] Find the equation of the curve of revolution of a coin leaving a chute. Finding the Sum of Arithmetico-Geometric Series [09/13/2004] Find the sum of the infinite series 1/7 + 4/(7^2) + 9/(7^3) + 16/(7^4) + ... I would also like to know if there is a general rule to find the sum of (n^2/p^n) for n = 1 to infinity. Finding the Width of a Corridor [11/13/1995] A steel girder 27 ft long is moved horizontally along a passageway 8 ft wide and into a corridor at right angles to the passageway. How wide must the corridor be for the girder to go around the corner? Neglect the horizontal width of the girder. Finding Volumes: Washer/Disc Methods [01/05/1998] I am having difficulties in the washer and disc methods of finding volumes, as in the problem y=x^2, x=3 about the y axis. Find Polynomial G(x) (Impossibility) [7/1/1996] For all real x, F(x) = x+3 and G(x) is a polynomial of degree two such that G(F(x)) = x+2. Find G(x). Find the Density Function [01/24/2002] Suppose X1, X2, X3 are independent and uniform on(0,1). Find the density function of S = X1 + X2 + X3. Find the Path and the Time Taken [10/17/2001] A man wants to cross a river 500m wide. His rowing speed relative to the water is 3000 m/hr. The river flows at a speed of 1200 m/hr... Find x in Degrees, not Radians [01/14/1998] I need to find the derivative of sin(x) when x is in degrees, not radians. Fixed-Point Theorem [05/02/2002] An intuitive reason why the theorem is true, and a proof. Floor and Mod Functions Discontinuous [10/10/2001] What is f(x) = x mod b for some fixed b? Formula for the Curvative of a Curve [10/10/2002] Is there a formula or theorem I can use to convince someone who believes a wall has only side that there is another side to it? Formula for the Trapezoid Rule [07/31/1999] I am writing a program to find the moment area of any shape... Formula to Sum a Series of Square Roots [07/03/2004] Is there a way to calculate the sum of the series sqrt(x) as x goes from 1 to n? Fresnel Integral of sin(x^2) [03/28/2002] I can not see how this integral from 0 to infinity can have any limit at all. If we used infinite series, we would not get a value for x = infinity. Frustum of a Pyramid with a Rectangular Base [02/20/2002] I am an engineer with a water treatment agency and need to figure the amount of water per foot of elevation in our reservoirs... Fuel Left in an Ellipsoidal Tank [10/19/2002] How much fuel is left in a tank at any depth, given that the tank is ellipsoidal? Functions of a Complex Variable [10/05/2002] Show that w=f(z*), where z*=x-iy and f is a differentiable function, is not an analytic function of z. Function X is a variable... [1/9/1995] Right now we are learning general exponential and logarithmic functions. In one of my homework problems.... The Gamma Function and Its Derivative [05/26/1998] Does n! = the integral from 0 to infinity of (x^n)(e^-x)dx hold true for all real numbers? If so, can we find the derivative of n!? Gamma Function Division [12/20/2005] Is there a formula for Gamma(n)/Gamma(m) for n and m having integer values >= 1 and m < n? Gas in a Cylindrical Tank with Hemispheric Caps [02/09/2010] Doctor Jeremiah uses calculus to calculate how much gas a large pill- shaped tank holds. General and Particular Solutions [01/08/1999] What is the difference between a general solution and a particular solution of a differential equation? Generalized Cubic Equation [05/22/2000] How do we find a generalized cubic rule for a family of cubics that cut through the point (1,1), have a gradient of 2 when x = 1, and have 1 stationary point? General Solution of dy/dt + y = t [10/25/1999] How can I find the general solution to the equation dy/dt + y = t? Generating the Volume of an n-Sphere [02/07/2002] Could you help me find an equation for the integration of a unit-ball in n-dimensions? Geometric Proof of a Limit [12/06/2003] Prove that lim[x->0](sinx)/x = 1 without using L'Hopital's rule. Goat and Silo [05/31/2001] A goat is roped to a point A next to a silo 30 ft. in diameter. The rope is 15pi feet long. How much area can goat graze? Goat tied to a barn [11/8/1994] If there is a goat tied to a rectangular barn on a 50 foot lead and the barn is 20 feet by 20 feet (floor), what is the maximum grazing area? Assume the goat is tied to a corner. The Gradient [06/03/1997] What is the geometrical interpretation of the gradient? Graphing Absolute Values [07/03/2002] I have a function, f(x), that I can graph, but I don't understand how to graph |f(x)|. Graphing Limits [09/12/2001] I was hoping you could explain the concept of "limits" and how to read them from graphs. Graphs and Gradients [05/13/2003] Sketch graphs of f and f' for f(x) = sin x and guess the formula for f'(x). Great Circle Parametric Equation [05/25/1998] How can you calculate specific points of a great circle on a sphere? Can you help me find the parametric equation? Half-Life of a Radioactive Substance [8/4/1995] The half-life of a radioactive substance is d days. If you begin with a sample weighing b g, how long will it be until c g remains? Halving and Halving Again - Zeno's Paradox [8/22/1996] Since we can never really get to zero by reducing something by halves, does that mean that we are floating on air? Harmonic Series [04/28/2003] Prove that if in the sum 1 + 1/2 + 1/3 + ... + 1/n we throw out each term that contains 9 as a digit in its denominator, then the sum of the remaining terms is less than 80. Heat Supplied and Heat Loss of a Furnace [05/17/2000] Heat is supplied by a furnace at a constant rate, but is lost at a rate determined by the difference between its temperature and the temperature of its surroundings... Helix Lying on a Cylinder [11/26/1997] I am trying to find a parametric equation for a helix (in 3 space) lying on the cylinder... History and Applications of the Natural Logarithm [03/02/1998] I'm so surprised at how often the number e comes up. Where did it come from? Who first derived it? Why is it so common in the field of biology? How a Calculator Determines Values of Trig Functions [03/19/2005] I'm interested in how my calculator finds the answer of sin(pi/4) or tan(pi/6), for example. Does it use power series? Page: []

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