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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? 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 non-Euclidean 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 high-school-level 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))/(2n-1)? 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 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 (1-cos 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(2-t) - 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 Multi-Variable 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). Limits of Sequences [02/25/2001] Is the limit of [(1 + 1/sqrt(n))^(1.5n)], as n goes to infinity, e? What is the limit as n goes to infinity of [(1 + a/n)^n], where a is not equal to 0? Limits of the Natural Logarithm [07/22/1998] Can you help us find the limit of x (ln x)^n as x goes to infinity, for all n? Do we use L'Hopital's Rule? Linearity and Concavity [12/07/2003] Why does a linear function have no concavity? Line Tangent to an Ellipse [03/29/2003] Find the equation of the tangent to the ellipse x^2 + y^2 = 76 at each of the given points: (8,2),(-7,3),(1,-5). Write your answers in the form y = mx + b. Logistic Growth of A Rumor Spreading [04/11/1998] Assuming logistic growth, find how many people know the rumor after two weeks. Page: []

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