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 TOPICS This page:   analysis    Search   Dr. Math See also the Internet Library:   analysis 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 Analysis Stars indicate particularly interesting answers or good places to begin browsing. Divide by 0 Undefined? [9/10/1996] When something is divided by 0, why is the answer undefined? Infinity over Infinity [4/10/1996] My teacher says that infinity divided by infinity equals one. I say that infinity over infinity is indeterminate... Infinity, Zero [1/4/1995] You can't divide by zero, but no one can actually prove WHY. . . I wanted to see a real proof first. . . We learned in trig that you can't raise zero to the zero-th power because zero would equal one, obviously. I realize infinity is not so much a number as an endless amount, but if there are an infinite number of numbers between 1 and 2, and an infinite number of numbers between 1 and 50, wouldn't the second infinity be bigger than the first? Line Segments and Size of Infinites [03/19/1997] Divide a line segment into three parts, one half and one a quarter the length of the line segment. Choose a point at random along this line segment. What is that probability that this point lands in the 1/2 segment...? Lines, Points, and Infinities [09/01/2001] What is the cardinality of the set of real numbers between 0 and 1? Is this cardinality less than, greater than, or equal to the cardinality of real numbers between 0 and 2? Patterns in Linear Systems [11/12/2001] Given the equation 2x+5y=8, with the coefficients increasing by 3 each time, create linear systems that are similar using equations such as 3x+4y=5 or 4x+6y=8. Point nine repeating equals one? [12/20/1994] When I learned how to convert repeating decimals to fractions, we were given an example in which .9 repeating equalled one. The problem I have is that I can't logically believe this is true, and I don't see an error with the math, so what am I missing or forgetting to resolve this? Proof of L'Hopital's Rule [12/23/1998] Can you show me a proof of L'Hopital's Rule and say how it relates to the different versions of the Rule? Rational and Irrational Numbers [11/12/1997] Which set is bigger, the set of rational or irrational numbers? Rational Numbers [11/24/1997] Which is greater, the number of rational numbers between 0 and 1 or the number of rational numbers between 0 and 2? 0 Raised to a Power [04/25/2002] What is the limit of 0^n as n approaches infinity? Can you explain why it equals zero or why it can't equal zero, or if it's undefined? 1 + 2 + 3 + 4 + ... Equals ... -1/12?! [09/18/2012] Doctor Vogler explains how functions extended by analytic continuation can be evaluated to produce counterintuitive results. Alternating Harmonic Series [11/18/1997] I am trying to find the proof for the sum of the alternating harmonic series. I did find out that it is ln(2), but please tell me why? Analysis and the Derivative [01/23/2001] Suppose that f:RtoR is differentiable at c and that f(c)=0. Show that g(x):=|f(x)| is differentiable at c if and only if f'(c)=0. Chaotic Functions [10/30/2000] Can you give some mathematical examples of chaos theory? Closure and Compactness in a Metric Space [10/08/2002] Regard Q, the set of all rational numbers, as a metric space, with d(p,q)=|p-q|... Show that E is closed and bounded in Q, but that E is not compact. Is E open in Q? Closure and the Reals [03/26/1998] Under what set of operations are the positive real integers closed? Compact Sets and Hausdorff Spaces [03/19/2003] How do you prove that every compact subset of a metric space is closed? Complex Numbers in Quadratic Equations [11/09/1999] How are imaginary numbers used in solving quadratic equations? How can solutions of this type be represented graphically? Continuity [11/24/2001] Suppose f and g are continuous on I = [a,b]... Prove there exists a k greater than 0 such that f(x) + k is less than or equal to g(x) for all x in I. Convergence of Sums [05/07/1999] Deduce that the following sum converges absolutely: Sum from 1 to infinity of (-1)^(n-1)/(n^2)! Convergent and Divergent Series [07/14/1998] I cannot seem to solve these problems... Countability [09/09/1998] How can I show that the rationals are countable and the irrationals are uncountable? Creating a Smooth Acceleration in Animation [05/09/2001] I am trying to figure out a way to set the value of X to achieve a specific difference between the last two sets in this problem... Definition of the Limit [11/05/2002] I need some help with the definition of the limit, particularly choosing delta for a given epsilon. Delta-Epsilon Limit Proofs [09/05/1998] Can you help me with some delta-epsilon proofs? How do you choose delta? Dense and Nowhere Dense Sets [04/25/1999] Can you define the mathematical terms 'dense' and 'nowhere dense'? Derivation of the Power Series of Cosine [1/22/1996] Would you please explain how the power series is derived from the cosine function and any other function? Deriving the Gamma Function [12/15/2000] How can you prove that sqrt(pi)/2 = (1/2)!, and what is a fractional factorial like that equal to? Descartes' Rule of Signs and Complex Roots [08/04/1998] Prove that if p and q are real and q is not equal to 0, the equation x^3 + px +q = 0 has two imaginary roots. Epsilon - Delta Proofs [1/23/1996] I'm confused about the f(x) in the epsilon function and the x in the delta function... Equations with Infinity [07/29/1998] How can you use infinity in maths equations? Is it like other numbers? Equations with Rational Expressions in Two Variables [12/07/2002] Determine all positive integers a and b that satisfy the equation: 1/a + a/b + 1/ab = 1. Eternity [12/30/1997] If you must choose from two alternatives, eternity or half of eternity, which is the best? Euler Formula: e^(pi*i) = -1 [6/5/1996] Why does e^(pi*i) = -1? 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. Explain Supremum [02/02/1998] Can you please explain, perhaps with an example, the concept of "supremum"? Factoring Quadratics [03/05/1998] Factoring quadratics that occur in fractions. Fibonacci sequence [1/28/1996] What is the explicit formula for the Fibonacci numbers? Fibonacci Sequence - An Example [05/12/1999] Glass plates and reflections. Page:  1  2  3 [next>]

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