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. S

    Square Root Problem: Equal Expressions?

    1. Homework Statement [/b] i have this thing: 2u\sqrt{}um is this expression the same as: 2u^3/2*m^1/2 Homework Equations The Attempt at a Solution
  2. S

    Linerization of square root of sin(2x)

    Homework Statement Find the linerization of square root of sin(2x) Homework Equations The Attempt at a Solution I don't even know how to start. What is linearization? Thanks
  3. O

    Cubed root denominator limit question

    Homework Statement Evaluate lim x->8 (x-8)/(cubed root of x) -2) Homework Equations The Attempt at a Solution I multiplied both numerator and denominator by (cubed root of x) +2. In the denominator, I wrote it as ((x^1/3)-2)*((x^1/3)+2) which simplifies to (x^2/3)-4. I have...
  4. S

    Integrating the Square Root: $\displaystyle \Large \int udv$

    Homework Statement http://img37.imageshack.us/img37/1237/63391287.jpg Homework Equations $\displaystyle \Large \int udv$ = uv - $\displaystyle \Large \int vdu$The Attempt at a Solution can i take this 3 out of the integral as well and make it 3/8 *$\displaystyle \Large \int _0^8 sqrt(64 +...
  5. M

    Calculating RMS Current and Phase Shift in an Inductive Circuit

    root mean square current?? Homework Statement A) If the voltage across the outlet terminals in your house is 110 Vrms at 60 Hz, and an ideal 5 H inductor is placed across the outlet terminals, what is the magnitude of the rms current flowing through the inductor? B) Assuming that the 110...
  6. Somefantastik

    Series Convergence: Does This Series Converge and What is the Sum?

    Homework Statement Does it converge, and what is the sum: \sum_{n=1}^{\infty}\frac{1}{n n^{\frac{1}{n}}} Homework Equations The Attempt at a Solution Please check my method and conclusion: Using the root test: \displaystyle\lim_{n\to\infty}\left|\frac{1}{n...
  7. M

    Square root and cube root question

    Homework Statement why is it possible to take the cube root of a negative number and not a square root of a negative number? Homework Equations The Attempt at a Solution
  8. M

    What is the solution to (x-7)^2=(x+3)^2?

    Homework Statement (x-7)^2=(x+3)^2 2. The attempt at a solution I squared both sides and received x-7=x+3 However, that cannot be correct because the variables cancel out which means there is no solution. The book shows that there is a solution of 2
  9. C

    Integral of Square Root of Sin(x)

    Homework Statement Find the Integral of \sqrt{sin(x)} Homework Equations none The Attempt at a Solution People say it's -2/3cos(x)^{3/2} which I don't think so or is it? thank you
  10. N

    Calculating RMS Using Integral Method

    calculate the RMS (root mean square) of this function. the period T=4 the formula is V_{rms}=\sqrt{\frac{1}{T}\int_{0}^{T}V_r^2dt} V_{rms}=\frac{1}{4}4\int_{0}^{T}(4t)^2dt} V_rms=\sqrt{s}=\sqrt{\frac{16}{3}} the solution says that they divide the graph into 4 traingles and they sum their areas...
  11. J

    Problem Calculating a limit with a square root, i'm stuck

    Problem Calculating a limit with a square root, I'm stuck :( Homework Statement The limit is equation 9-t / 3-sqrt(t) as t approaches 9 I'm stuck on the how to simplify this? Thanks for any help. Homework Equations The Attempt at a Solution
  12. T

    First step to proof of convergance using Newton's root finding method

    Suppose I am looking for the root of a function of the form: f(x)=x ^{m}-c, where c,m>1. Suppose I take my first guess to be x _{0}=c. Then using Newtons method my next guess will be given by: x _{n+1}=x _{n} - \frac {f(x _{n})}{f'(x _{n})}. From this, or thinking about this...
  13. E

    Proving the Equivalence of Square Root of Complex Numbers

    Homework Statement show that \sqrt{1+ja} is equivalent to \pm(1+j)(a/2)^{1/2} with a>>1 Homework Equations Euler's formula? The Attempt at a Solution with a>>1 |z| = \sqrt{(1 + a^{2})} == a lim a-->infinity arctan (a/1) == \pi/2 \sqrt{z} = \sqrt{(ae^{j\pi/2})} \sqrt{z} =...
  14. Char. Limit

    Is Every Root of 2 Higher Than 1 Irrational?

    I was thinking on the square root of 2 being irrational proof... and I got the idea that you could use the same idea for every root higher than two. The cube root, the quartic root, the quintic root, etcetera. (Obviously assuming the roots are natural numbers.) As a reassurance I'm not crazy...
  15. G

    Why root mean square for temperature?

    I was wondering why it is that when the temperature of something is being described, the root mean square speed of its atoms is used and not simply the mean speed. Why is the RMS more meaningful/useful when describing these things than the mean? Thanks.
  16. M

    Continuous square root function on the space of nxn matrices

    Homework Statement Hi again all, I've just managed to prove the existence (non-constructively) of a 'square root function' f on some open epsilon-ball about the identity matrix 'I' such that [f(A)]^2=A\qquad \forall\, A \,\text{ s.t.}\, \|I-A\|<\epsilon within Mn, the space of n*n matrices...
  17. T

    Root mean square interpretation

    i am working in control theory problem where at the end i get error signals and i am trying to classify this signals, i choosed easy implementation because of limitaion of microcontroller which i will program later. the easiiest way was to calculate the Root mean square of the random signals...
  18. T

    Root mean square speed and ideal gases

    Homework Statement At 318 K and 1.04 x 10-2 atm, the density of a gas is 1.75 x 10-5 g/cm3. (a) Find vrms for the gas molecules. (b) Find the molar mass of the gas. Homework Equations vrms= sqrt (3RT/M) pV=nRT pM=dRT pV=(m/M)RT The Attempt at a Solution the main problem i...
  19. C

    Learn How to Calculate RMS and Avoid Mistakes: Root Mean Square Help

    Hello, For 1 and 2 I want to calculate rms then x_{rms}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}x_i^2}\Rightarrow x_{1,2}=\sqrt{\frac{1}{2}(1^2+2^2)}=\sqrt{\frac{5}{2}} And also x_{rms}=\sqrt{\frac{1}{x_2-x_1}\int_{x_1}^{x_2}f^2(x)dx} For the function f(x)=x, x_1=1, x_2=2...
  20. S

    Validating the Limit of the Square Root Function

    Could someone help me with this? I feel it should likely be easy, but I'm baffled anyway: Homework Statement Prove the validity of the limit lim x -> x_0 sqrt(x) = sqrt(x_0) Homework Equations use definition of limitThe Attempt at a Solution Generally confused. I start with |sqrtx - sqrtx0|...
  21. D

    Writing 2^{1-i} using Euler's Formula

    Homework Statement Use Euler's formula to write 2^{1-i} in the form a+ib. The Attempt at a Solution I know this has to be so simple because I could do this easy if the question was to write e^{1-i} in the form a+ib using Euler's. So what I do not understand is how does 1-i being...
  22. J

    Solving for x with a Square Root Sign: Help Needed!

    Does anyone know how to solve for x in the following equation: x + \sqrt{x} = 6 I don't know how to solve for x with eq'ns like this, and I'm studying inverse fxns right now, so I'm told that's what I'm supposed to do. The square root sign is throwing me off. The first time I tried...
  23. T

    Limit of the nth root of (n ln n)

    Homework Statement Find lim_{n \rightarrow \infty} \sqrt[n]{n ln(n)}. Do not use L'Hospital's Rule or Taylor Series. Homework Equations The Attempt at a Solution I suspect I need to set up some inequality for this and then apply Squeeze Theorem. But I can't find any inequality...
  24. J

    Easy question about the root (of a real number)

    [SOLVED] Easy question about the root (of a real number) Hi, I'm a bit embarresed to ask this but does anybody know how to get this: \sqrt{3 - 2\sqrt{2}} = \sqrt{2} - 1 ?
  25. DocZaius

    Notation for Principal Square Root?

    Hello, I was just wondering if there is a special notation for a principal square root... I suppose using absolute value would work.. \left|\sqrt{9}\right|=+3 But it doesn't seem as fitting as an actual special square root symbol. Maybe something like this? \sqrt[+]{9}=+3 Also...
  26. I

    Square root of Dirac Delta function

    Homework Statement I wonder how to deal with the square root of Dirac Delta function, \sqrt{\delta(x)}. Actually, this comes from a problem which asking readers to calculate the wave function of a free particle and of a harmonic oscillator at time t, provided that the wave function at time...
  27. J

    Square root of 1 with mod how to prove it?

    I know that if n is odd and has k distinct prime factors, then the number of roots, x^2 = 1 (mod n), is equal to 2^k. However, I don't know how to give a formal proof to it. I simply want to bypass the generalized form x^2 = a (mod n). How can I prove it directly? Thank you.
  28. W

    Question about the limit of a square root

    Hello! I got the following exercise: \frac{lim}{x\rightarrow6-} {\sqrt{3x-18}} Now, since I need to evaluate the limit from the function coming from the left to the right that means that I can evaluate the function using x as a value very close to 6, but not six, right? So, since I would...
  29. S

    Proving a limit theorem of a sequence (square root)

    Homework Statement given the sequence {a_n} converges to A (non zero), show sqrt(a_n) = sqrt(A) Homework Equations The Attempt at a Solution I've tried to expand |sqrt(a_n) - sqrt(A)| as |a_n - A|\|sqrt(a_n) + sqrt(A)| since that gives me the numerator to work with, but I can't...
  30. N

    Is there a way of proving that all positive numbers have a real square root?

    Homework Statement My prof showed us the proof that sqrt2 is not a rational number. She said, however, that we haven't proved that it is irrational, because we haven't proved that sqrt2 exists. How would we go about proving this? Homework Equations N/A The Attempt at a Solution...
  31. Y

    Integrate x^2 /square root (x^2 +1)

    Hi, the question is integrate x^2 /square root (x^2 +1). I tried to do it but i was stucked in the very last step.at the end,I got x/2 * cosh(arcsinh x) + 1/2 * arcsinh x - arcsin (square root (x^2 + 1)) +C. I dunnoe how can I simplify cosh(arcsinh x) into simplier form in term of x. I hope...
  32. S

    How Do I Solve This Complex Square Root Equation?

    Homework Statement Can someone advice me how to solve this square root equation? n_{0}=1.5*10^{15}+\sqrt{(1.5*10^{15})^{2}+[(0.05)n_{0}]^{2}} The answer should be n0=3.0075*1015 I can't figure out how to open up the square root to solve the equation for n0. Stuck here staring at the...
  33. E

    Square Root Method - Fractions

    Homework Statement x^2 - 1/2x - 3/16 = 0 The Attempt at a Solution Actually, I don't know where to start since I have fractions.
  34. E

    Limits of expression with square root

    I am looking at the derivation for an expression that relates the concentration of an oxide to time. It appears that to do this, the author takes the limit of sqrt(A+Bt), where A and B are constants as t approaches zero and infinity. Is there an easy way to do this without making assumptions...
  35. E

    Solve Square Root Method: (x-1)^2 = 4

    Homework Statement (x - 1)^2 = 4 The Attempt at a Solution This is what I've done (x - 1)^2 = 4 Everything inside parenthesis goes to: ^2 x^2 - 1^2 = 4 now we got x^2 - 1 = 4 Now (I think) I use the square root method x^2 - 1 = √4 x^2 - 1 = 2 Now I factorize: (x - 1) (x +1) = 2 This is...
  36. E

    Inverse function containing square root

    Homework Statement Given f(x) = -x2 - 2x + 3, x < -1 Find f-1. Find f-1f. Homework Equations Nil. The Attempt at a Solution Actually I worked out much of the question already, and I already know that f-1f: x -> x. The problem is, I can't seem to get f-1f(x) = x on...
  37. C

    Derivative of a square root fraction. HELP

    Homework Statement What is f'(x) of f(x) 1/sqrt(2x)? 2. The attempt at a solution In applying the problem to the derivative formula: (1 / sqrt(2(x + h)) - 1 / sqrt(2x)) / h I multiplied the problem by a special form of one but that only put the rationals on the bottom of the...
  38. D

    Principal root of a Complex Number

    Homework Statement Find all the roots in rectangular coordinates, exhibit them as vertices of certain squares, and point out which is the principal root. The Attempt at a Solution The problem is (-8 -8\sqrt{3}i)^{\frac{1}{4}} and I found the four roots easily to be \pm(\sqrt{3} -...
  39. T

    Why Can't You Cancel Out the Square Root and Square in a Square Root Problem?

    Homework Statement Can someone explain to me how |-4|= \sqrt{(-4)^{2}} I'm wondering why you can't cancel out the square root sign and the square above the -4, to leave you with -4. The Attempt at a Solution I know this has something to do with the absolute value of -4, being 4, but...
  40. D

    Iterative square root? sqrt(2+sqrt(2+sqrt(

    The other day I was playing with my calculator and noticed that \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+...}}}} \approx 2 But, what is that kind of expression called? How does one justify that limit? And, to what number exactly does converge, for example...
  41. K

    Solving Root Finding Problem with Sparse Matrix | Krindik

    Hi, While trying to simplify a solution I came up with the following sparse matrix but don't know how to solve it. [A(t)][X] = 0 $\left( \begin{array}{ccccc} A_0(t) & 1 & 1 & ... & 1 \\ A_1(t) & 1 & 0 & ... & 0 \\ ... & ... & ... & ... & ... \\ A_{n-1}(t) & 0 & ...
  42. W

    How does \sqrt{1+((x^2)/(4-x^2))} simplify to 2 times\sqrt{1/(4-x^2)}?

    1.I can't figure out how the \sqrt{1+((x^2)/(4-x^2))} simplifies to 2 times\sqrt{1/(4-x^2)} I have tried rewriting it in different ways, but I can't see how it simplifies. \sqrt{x^2 + 1/4-x^2}
  43. S

    Norm of a function ||f|| & the root mean square of a function.

    norm of a function ||f|| & the "root mean square" of a function. How do I explain the connection between the norm of a function ||f|| & the "root mean square" of a function. You may like to consider as an example C[0,\pi], the inner product space of continuous functions on the interval [0,\pi]...
  44. N

    Can Ratio and Root Tests Determine the Convergence of Complex Series?

    1. \sum_{n=1}^{\infty}ntan\frac{1}{n} dont know where to start here 2. \frac{1*3*5*****(2n-1)}{n!} \frac{2n-1}{n!} \frac{2(n+1)-1}{(n+1)!}*\frac{n!}{2n-1} \frac{2n+1}{(n+1)(2n-1)} ->0 my book is showing divergence
  45. N

    How can I integrate the composite root integral \int\sqrt{40t^2+e^t^2}dt?

    Homework Statement \int\sqrt{40t^2+e^t^2}dt That should be e^t^2. How would I go about doing this?
  46. J

    Complex Numbers- Square root 3i

    (1- sqrt 3i) ^3 I am having trouble solving the sqrt 3i part. I think I need to use de moivres theorem but I am unsure. If someone could push me in the right direction that would be a massive help. Thanks.
  47. S

    Why the square root of the determinant of the metric?

    Hi, We use as an integration form in Riemannian geometry the covariant \int \sqrt{g}d\Omega I understand how this is invariant under an arbitrary change of coordinates (both Jacobian and metric square root transformation coefficient will cancel each other), what I don't understand is why don't...
  48. K

    Why Am I Stuck on My Root Locus Design Problem?

    Homework Statement The Attempt at a Solution Hi, I’ve been studying Root Loci for almost 3 months now, on and off, so I know most of the methods involved with it. I’m still pretty much new to the subject still as I’ve recently hit a problem with this exercise that I’ve been working...
  49. S

    Find Other Roots of a3-3a2+a+5=0 Given 2-i

    Homework Statement Given one root of the equation, find the others. a3-3a2+a+5=0 Given root: 2-i The Attempt at a Solution I know the answers, which are 2+i and -1. And I understand how to get the 2+i since when you square root anything, the answer can be positive or negative, but I have...
  50. I

    Square root operation and scales

    this is a strange problem easy to solve but I am having trouble understanding it intuitivly. Assume we choose a location point and name it 0. Next, in arbitrary direction and distance we place the number 1. Hence, we have created a scale(number line) that extends as much as we like. Now we...
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