Ask Dr. Math High School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

 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? Permutation and Combination Equality [07/18/1999] Prove that (nC0)^2 + (nC1)^2 + (nC2)^2 + ... + (nCn)^2 = (2nCn), where nCi = n!/((n-i)!*i!). Picard's Method [08/10/1997] Can you tell me about Picard's iteration method of solving differential equations? Plane Flying Parametrically [06/28/1999] How can I find out when a plane, whose position approaching an airport is described parametrically by P_t = (1000,500,900)+ t[-100,-50,-90], will be closest to the traffic control center, located at (24,11,13)? Point of Inflection [05/17/1997] The cubic polynomial h(x) = x^3 - 3bx^2 + 3cx + d has a local maximum and a local minimum... Point on a Parabola [1/9/1995] How do you find the point on the parabola y = x^2 nearest the point (- 3,0)? Points of Intersection [08/31/1997] Estimate all points of intersection of the graphs f(x) = x + sin x and g(x) = x^3 by using a calculator or computer. How do you know you have found them all? Polar Coordinates [11/4/1996] Find the polar equation of x^3+y^3=3axy with x+y+a=0 as an asymptote. Polar Coordinates for Velocity and Acceleration of a Particle [03/11/1997] I know that velocity components are dr/dt and rdo/dt and that components of acceleration are d^2r/dt^2 - r(do/dt)^2, etc. I would appreciate any help at all in understanding how these are generated and/or how to use them. Position Function of a Moving Particle [9/9/1996] A particle moves on a straight line with a velocity v(t)=sin(w)cos^2w; f(0)=0; w is constant; find f(t). Possible Proof That 1 + 1 Does Not Equal 2 [04/19/2001] I just want verification... would this proof work? Power Series for Sine and Cosine [10/12/2000] Can you explain, without using calculus, how to get the power series for sine and cosine? Pre-calculus Function Question [2/8/1996] Does the function f(x)=3De^(1/x) have a local minimum? Primitive function [6/11/1996] Give a primitive function of (sin x) / (ln (2 + x^2)). Projectile Velocity and Vectors [5/7/1996] If the initial velocity is 834 meter^2/sec at an angle of 60 degrees, and x is 21,000, at what time, t, is the object at x = 21000 meters? Proof by First Principles [11/16/2001] How can I prove by first principles that the derivative of tan(x) is sec^2(x)? Proof for the Radius of Curvature [08/17/2003] The equation of a circle of radius R centered at the origin is x^2+y^2 = R^2. Demonstrate that the radius of curvature is equal to R. Proof of a Bounded Series using the Binomial Theorem [6/6/1995] Prove that (1+1/n)^n is bounded from above. Proof of Absolute Value, Division [7/16/1996] If y does not equal to 0, prove that |x / y| = |x|/|y|. Proof of Cosine of 36 Degrees [11/26/2001] Prove: cosine {(pi)/5} = {1+5^(1/2)}/4. Proof of Derivative for Function f(x) = ax^n [01/14/2004] Is there a way to prove or show why the derivative of ax^n turns out to be anx^(n-1)? Proof of Integration by Parts [02/06/2001] How do you derive the formula for integration by parts? Proof of Series ln(1+x) [11/15/2001] I need to show that the series ln(1+x) equals x-x^2/2+x^3/3-x^4/4, and so on, whenever x is between -1 and 1. Proof of Stirling's Approximation [03/09/2006] Can you prove that lim ((e^n)(n!)) / ((n^n)(n)^1/2 = (2pi)^1/2 ? Proof of Tangent Double Angle Identity [7/16/1996] I would like to see the proof of the tangent double angle identity. Proof of the Chain Rule [09/06/2004] I am using the Chain Rule (dy/dx = dy/du * du/dx) in my math class, and I would like to see it proved, which we don't do in class. Proofs of e [03/21/2002] I found out that the definition of e is: e = lim, as n approaches infinity (1+1/n)^n. Is there a proof for this or for 1+2(e-1/n)? Proof that 2 Equals 1 Using Derivatives [05/10/2000] If d(x^2)/dx = d(x+x+...+x)/dx, then 2x = 1+1+...+1 = x. What is the error in this "proof"? Proof that INT(1/x)dx = lnx [11/08/1996] How do you integrate (1/x)dx? Proving Limits at Infinity Using the Formal Definition [04/11/2004] We are required to find a limit (informally), then prove that our answer is correct by using the formal definition of limits. I'm not sure I'm on the right track. Proving Limits Formally [01/04/1999] Given a sequence, I can guess what the limit it. How do I actually prove my guess is the limit? Proving That d(e^x)/dx = e^x [06/30/1999] How can I find the derivative of y = e^x, using the definition of the derivative? Proving the Derivative of e^x Is e^x [02/20/2006] What is the delta x proof of (dy/dx)e^x = e^x? Ptolemy's Theorem and Double-angle Formulas [7/11/1996] Is it possible to show the formula Sin(A-B), Cos(A+B) or Cos(A-B) using Ptolemy's Theorem? Quadratic Extrema [07/20/2002] Can you tell me how to find the minimum or maximum of a quadratic function? Quadratic Function and Diagonals of a Diamond [6/14/1996] The sum of the two lozenges (diagonals of a diamond) are maximum when the angle between the longest lozenge and the side of the diamond is 30 degrees, diamond side length = sqrt 2... Quotient Function Mnemonic [03/11/2002] Help me to differentiate the following: x/((x^2)-4). Raabe's Theorem [8/23/1996] Regarding Raabe's result for the convergence of a numerical series of non-negative terms - I am looking for is a convergent series having m = 1. Radian vs. Degree, Sin Derivatives [10/23/2001] Why do you get a different answer when you ask your calculator for the derivative of sinx in degree rather than radian mode? Radius of Curvature [07/23/2003] I have several ellipses whose major and minor diameters I know, but I have no information about their foci. Range of rational functions [12/1/1994] Given the following rational function: f(x)= (x-1)/(x^2+3x-1), how do you find the range? Our book gives the answer of: (neg infinity to 0.12] U [0.65 to pos infinity). Page: []

Search the Dr. Math Library:

 Search: entire archive just High School Calculus Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

[Privacy Policy] [Terms of Use]

© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/