Root Definition and 944 Threads

In vascular plants, the roots are the organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They most often lie below the surface of the soil, but roots can also be aerial or aerating, that is, growing up above the ground or especially above water.

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  1. C

    Differentiation problem square root function

    I'm on mobile so I can't use latex. Differentiate: g(x)=√(4-x^4) , x is a set of [-√2, √2] and determine the domains. So I got the derivative which is, g'(x)=(-4x^3) ^1/2 What should I do with the -+√2 ? I don't know what to do next
  2. Twinflower

    Deriving a root and a fraction

    Homework Statement Derive y= \sqrt(2x^4) - \frac{5}{3x^2} The Attempt at a Solution I am still at the first part of the function (the root): First I tried to derive inside the root like this: \sqrt(2x^4) = \sqrt(8x^3) = 2 \sqrt(2) \times \sqrt(x^3) = \sqrt(2) \times x^2...
  3. 1

    Newtons Method and Finding the 5th root

    Homework Statement Find the 5th root of 36 accurate to four decimal places Homework Equations xn+1 = xn - f(xn)/f'(xn) The Attempt at a Solution First I attempted to write the fifth root of 36 in exponential form as show below: Let the 5th root of 36 = x Let f(x) =...
  4. K

    What are the matrices that have only one square root?

    Does this have to do with the eigenvalues?
  5. K

    Square Root of a 2x2 Matrix (by diagonalization)

    Homework Statement Show that the -1 -2 4 -1 2x2 matrix has one square root. Homework Equations det(A-λI) to find Eigenvalues (A-λI)v=0 to find Eigenvectors A1/2 = V D1/2 V-1 to find the square root of A where V is the created matrix with the...
  6. D

    Fast algorithm to find root of strictly decreasing function

    What is the fastest algorithm to find the closest root (such that the function value at that point is positive to an error but never negative, if not exactly zero) for a strictly decreasing function?
  7. M

    A limsup inequality (showing that the root test is stronger than the ratio test)

    Homework Statement Show that if a_n > 0 for all n, \liminf{\frac{a_{n+1}}{a_n}} \leq \liminf{a_n^{1/n}} \leq \limsup{a_n^{1/n}} \leq \limsup{\frac{a_{n+1}}{a_n}}Homework Equations \liminf{a_n^{1/n}} \leq \limsup{a_n^{1/n}} \liminf{\frac{a_{n+1}}{a_n}} \leq \limsup{\frac{a_{n+1}}{a_n}} These...
  8. S

    Newton's Method for Root Finding - Infinite Loop

    1. Construct a function f (x) so that Newton's method gets 'hanging' in an infinite cycle xn = (-1)n x0 , no matter how the start value x0 is chosen. 2. Homework Equations : xn+1 = xn - f(xn) / f'(xn) The Attempt at a Solution xn+1 = xn - f(xn) / f'(xn) = (-1)n+1x0 = (-1)nx0 -...
  9. N

    Determine the exact value of (Square Root of Square Root)

    Determine the exact value of... (Square Root of Square Root) I was looking through my textbook and saw a interesting question, I attempted but couldn't get it. (The Answer in Back of Text Book Was Different From Mine..) Question Determine the exact value of... √10+√10+√10... I...
  10. M

    Square Root of a Quantity of X

    How does one calculate the square root of a quantity of x e.g. \sqrt{25x}? Also could you equate 5x^{2} to 25x? Just a thew random queries going around my head. NOTE: I'm 14.
  11. B

    How cubed root of x is not differentiable at 0

    I know that it isn't. I just want to know how I could, step by step, prove that this function is not differentiable at x=0.
  12. M

    Why the principal nth root is unique ?

    Why the principal nth root is unique ? I mean in the definition of the princibal nth root it says: let x be a real number and n is natural number n \geq 1.if n is odd , the principal nth root of x denoted \sqrt[n]{x},is the unique real number satisfying (\sqrt[n]{x})^{n} = x.if n is even , the...
  13. A

    Rearranging equation with a square root

    " Solving this for κ, substituting into (1), and rearranging for G, the result is: " I am trying to rearrange the first equation to make κ the subject and I get: http://www.adamrapley.com/eqn1/CodeCogsEqn%20(6).gif http://www.adamrapley.com/eqn1/CodeCogsEqn%20(5).gif...
  14. M

    Intergation problem involving square root

    Homework Statement \int_{1}^{3}\sqrt{y^2+\frac{1}{2}+\frac{1}{16y^4}}dy Homework Equations The Attempt at a Solution I don't know what to do with this integral, but i do feel like this can be simplified into something much simpler. I tried rewriting it as...
  15. A

    How can I solve complex root problems without using De'Moivre's theorem?

    Homework Statement What is the square root of z=-9Homework Equations The Attempt at a Solution Is it possible of me to not use De'Moivre's theorem to solve this question?? Solution : z= \sqrt{-9} z=\sqrt{9} x \sqrt{}-1 z=\pm3 i Will this method be acceptable?? Is this still under the topic...
  16. D

    Proof of square root properties

    Homework Statement \sqrt{\sum}x^{2}_{i}\leq\sum|x_{i}|\leq\sqrt{n}\sqrt{\sum}x^{2}_{i} *The sums are all from i=1 to n.* Homework Equations The Attempt at a Solution I'm very new to proof-based math, and just looking for some help to get started with this one. Thanks in advance.
  17. S

    Square root in suqare root in square root in square root in

    square root in suqare root in square root in square root in... Homework Statement Find the value of: \sqrt{1001\sqrt{1002\sqrt{1003\sqrt{1004...}}}} Homework Equations exponential and surd The Attempt at a Solution I tried to square it but didn't find any patterns because the...
  18. R

    Can a Square Root Function Have Two Slopes and Exist in the Fourth Quadrant?

    y = \sqrt{x^2- 2x + 1} The y' is always the slope right? Then if we simplify the equation y =\sqrt{(x-1)^2 }----or---y = \sqrt{(1-x)^2} y = x - 1 y = 1-x Checking:---------------Checking: \sqrt{(x-1)^2}-------------\sqrt{(1-x)^2}...
  19. X

    Differential eq with square root numerical

    Hi! I have to solve a system of two coupled nonlinear ordinary differential equations. In the function that defines the system there are terms with square root of the dependant variables. I tried to solve the system numerically but in the nmerical solution I get violent oscillations. Then I...
  20. W

    What is the Sum of the Reciprocals of Variables in Solving Cubic Root Equations?

    Hi, can you help me with this problem? a = \sqrt[3]{1 - 4b - 4c} b = \sqrt[3]{1 - 4c - 4a} c = \sqrt[3]{1 - 4a - 4b} Find \dfrac{1}{a} + \dfrac{1}{b} + \dfrac{1}{c} Thanks
  21. D

    How to find the root of a quadratic formula

    Homework Statement (A) For what value of K does the equation 2x^2-10x +8 = K have a repeated root? Use the quadratic formula to find the root. (B) Choose a value for K so the equation has no real roots, Use the quadratic formula to prove that this equation has no real roots for your...
  22. J

    Integration of a Square Root including constants

    1234
  23. M

    Is There a Method to Find the Square Root of Confusing Algebraic Expressions?

    I found a way to find the square root of an expression which is confusing to me. Is anyone familiar to this method? And my main question... will it be useful?
  24. W

    Root Locus Sketching: Re-arrange & Sketch for Parameter "a

    Homework Statement Re-arrange the open-loop transfer function and sketch the root locus for the system for variation of the parameter 'a' from 0 to infinity. Homework Equations G(s)H(s) = 10(s+a) / [s(s+1)(s+8)] The Attempt at a Solution my problem is that i don't know how to re-arrange...
  25. M

    Square root of a rational quantity: Algebra

    Why arnt the two terms eqaul even though the square root of m was solved properly? And is this a general rule?
  26. A

    Simple algebra and square root help.

    Homework Statement is there no square root for a negative number? is there no solution for this? q=-1 r=2 the square root of 2q - 5r The Attempt at a Solution 2x-1 - 5x2 = -12 sqaure root of -12? my calculator doesn't come up with a answer for the square root.
  27. sankalpmittal

    The square root yields only one value ?

    The square root yields only one value !? One guy advanced and asked me the question with an intention to judge my skill - " What is the value of x , if x2=4 " I , without any reluctance replied rather confidently - " Ha , its simple x will have 2 values : +2 and -2 " He laughed hard and said...
  28. M

    Interesting plot of an implicit equation with square root of signum functions

    Hello, recently, I have found so called Batman graph and equation, which basically plots Batman sign. I have even found Python code that plots this implicit equation. Code can be found here: . And the equation is given here: [url]http://i.imgur.com/CNy9J.jpg If you look closelx...
  29. 5

    Simplifying the Derivative of the Square Root of a Sum Containing a Square Root

    Homework Statement EDIT: Ahhh, my apologies. At first, I thought it appropriate for the non-calculus sub-forum, but by the title it really does not, XD. I also can't seem to find how to remove it. The question really does not require calculus, though! Basically, the problem of finding the...
  30. Z

    Ratio & Root Tests: Convergence & Divergence

    Homework Statement Test for convergence and divergence. Homework Equations \sum_{i=1}^{n} \frac{n!}{3^n} \sum_{i=1}^{n} \frac{1}{{(log (n))}^{1/n}} The Attempt at a Solution For the first one I get \frac{(n+1)}{3} After applying the ratios. Taking the limit as n approaches infinity, it is...
  31. C

    Root Test Question: Baby Rudin Example 3.35

    Homework Statement Consider the following series (Baby Rudin Example 3.35): \frac{1}{2} + \frac{1}{3} + \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{2^3} + \frac{1}{3^3} + \ldots We have to apply the root test. 2. The attempt at a solution \sqrt[n]{2^{-\frac{n+1}{2}}} =...
  32. V

    Integral of Bessel function, square root and gaussian

    Hi! Does anyone know how to solve the following integral analitically? \int^{1}_{0} dx \ e^{B x^{2}} J_{0}(i A \sqrt{1-x^{2}}), where A and B are real numbers. Thanks!
  33. W

    C/C++ How Can You Learn ROOT If You're New to C++?

    How to learn ROOT ?? What do i need to learn ROOT ? and what do i need in c++ to learn ROOT?
  34. A

    Prove that 111x^111+11x^11+x+1 has only one real root

    Homework Statement Prove that the function 111x^111+11x^11+x+1 has exactly one real root. The Attempt at a Solution Well, I know how to prove this. f is continuous because It's a polynomial. f(-1) equals -111-11-1+1 = -122 < 0 and f(0) equals 1. therefore, It satisfies all conditions...
  35. J

    What is the equation for a 2-norm of 1 in a 2-dimensional vector?

    Homework Statement I have a homework problem that asks the following: R^2 is a 2 dimensional vector. I know how to calculate vector norms, but I'm not sure how to approach the rest of the problem. Can anyone help me out with this problem or point me in the right direction?
  36. B

    Is √N Always Irrational for Non-Square Integers?

    I came across this question. How do you show that √N is irrational when N is a nonsquare integer? Cheers.
  37. B

    Continuous fractions for root 2

    Hi all, Could anyone guide me on the following prove √2 = 1+1/(2 + 1/(2+ 1/(2+ 1/(2+···))))
  38. C

    Root test vs. ratio test question

    I am doing the following practice problem in prep for an exam: sum from n=0 to infinity: (3^n)/(n+1)^n The book says to use the ratio test on it, which I did, but would the root test also apply to this?
  39. A

    Sketch this curve (two multipled root functions)

    Homework Statement Sketch the curve defined by g(x) = x^{1/3}*(x+3)^{2/3}Homework Equations First Derivative Second DerivativeThe Attempt at a Solution I attempted to use the algorithm for curve sketching: 1) Find the intercepts 2) First Derivative; look for extrema and points where f'(x) DNE...
  40. U

    Integrate ln(cube root (2+y^3)) dydx

    Homework Statement integrate ln(cube root (2+y^3)) dydx with limits of y =sqrt (x) to 1 of x from 1 to 0 Homework Equations integral of ln x= x ln x. This ends up being very convoluted, haven't even begun to insert limits The Attempt at a Solution
  41. M

    Difference between unit-fractional exponent and root sign

    We were having our maths class a weeks ago and while studying quadratic equations our teacher asked us if there was an difference between x^{1/2} and \sqrt{x}. Up until then I had always assumed them to be the same thing. However he said that there was a difference and said that he would tell...
  42. S

    What is the Modulus of the Square Root of a Number?

    Consider this function: (x^2)^0.5 My textbook considers this to be |x| (modulus of x). Is it correct? x^2 gives a positive quantity.On taking square root of that,we'll get either -x or +x. So why modulus? Also, (x^0.5)^2 This is modulus isn't it? Thank You
  43. E

    If a+bi is a root of F, then a-bi is too

    Homework Statement Given f\left(x\right) \in \mathbb{R}\left[x\right], if a + bi is a root of f\left(x\right), then a - bi is a root of f\left(x\right) as well. Homework Equations Factor Theorem: if f\left(x\right) is a polynomial over a ring with identity, then a is a root of...
  44. J

    Root Locus: Plotting for k=1.33 & Finding Equivalent Damping Coefficient

    I was told to plot a root locus(by hand) of the open loop transfer function: H(s)G(s)= (s+2)/(s^2 + 2s + 3) and for a value of k=1.33 determine the location of the root, then find the equivalent damping coefficient. After several attempts i was able to draw the...
  45. O

    Finding the Root Mean Square Speed of Methane at 50°C

    i asked to find the root mean square speed of Methane in temperature of 50 degrees Celsius. so i have an dilemma which formula i need to use, so in the picture you can see the 2 formula that i have doubts. thanks.
  46. D

    Learning ROOT for Research: A Beginner's Guide

    Hello, this is my frist thread so I'm sorry if this is in the wrong place, but the other forums didn't seem to be as relevant. I'm trying to get a research position over the summer and I need to teach myself how to use Root, I have programming experience with Java (although it has been a...
  47. N

    How do I solve this root integral with reduction formulae?

    \intop_{-\pi/2}^{+\pi/2}\sqrt{(144sin^2t+6)cos^2t}dt how to approach it?
  48. J

    How Is the Square Root of 6 Derived Using the Square Roots of 2 and 3?

    Square Root of 6 <math>\sqrt{6}=\frac{sqrt{2}sqrt{3}}<\math>
  49. N

    How do you integrate \(\int \sec^{2n+1} x \, dx\)?

    \intop_{-\pi/2}^{+\pi/2}\sqrt{(-6sin2t)^2+\sqrt{6}(cost)^2}dt how to solve it? i tried by parts and it looks very bad and complicated edit sorry i copied the wrond integral now it fine
  50. T

    Convergence of a series by root test

    Homework Statement Does the series: sum from 1 to inf. (n+2)/(n+1) converge? If so does it converge absolutely? Homework Equations Ratio test for series The Attempt at a Solution I found this series to converge using the root test, (.jpg attached) however wolfram alpha...
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