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    Reaction between water and chromium metal

    Hi there, How to write the reaction between water and chromium metal under standard (i) acid and (ii) base condition? Cr + 3H2O ----> Cr(OH)3 + 3e- + 3 H+ (acid condition) basic solution ??? Please help
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    The different between the work (PV ) in ΔU and the work (PV ) ΔH

    By definition ΔU = q+PV ΔH = ΔU+PV Well, what are the different between the work (PV ) in ΔU and the work (PV ) ΔH then ? thank you
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    Limit of sequence lim n (1-cos(2/n))

    1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution above picture !! Exam in 3 hours :( please help
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    Laplace transform solve integral equation

    1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution The answer is y(t) = t^{4}+\frac{t^{6}}{30} Don't know what to do next any advices please
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    Trigonometry identity sin(pi)cos(wpi)+cos(pi)sin(wpi)

    1. Homework Statement Hi guys, How can sin(∏)cos(ω∏)-cos(∏)sin(ω∏) = sin(ω∏)? please guide me trigonometry identity to apply with this? 2. Homework Equations 3. The Attempt at a Solution
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    Fourier integral representation of function

    1. Homework Statement How can I get to that answer? 2. Homework Equations 3. The Attempt at a Solution I'm stuck dont know how to get to the answer that I got from wolframalpha. there is no solution there unfortunately. I know how to get to that denominator w^2-1 but I dont know how...
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    Square wave Fourier series

    1. Homework Statement what values does the Fourier series for f(t) converge to if t = 0 and t = 2? 2. Homework Equations 3. The Attempt at a Solution My answers the red rectangles for the even function t=0 >> 1 and t=2 -->1.5 and odd function t=0 >> 0 and t=2 -->1.5 because at...
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    Fourier of Half-Wave Rectified

    1. Homework Statement How did \frac{1}{2}x come from at k=1? 2. Homework Equations 3. The Attempt at a Solution because k=1 will make the first term at denominator 2(k-1) = \frac{0}{0}
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    Fourier series (2 same functions different inequality signs)

    1. Homework Statement these two functions will give the same Fourier series? because when I write the graph they look the same? 2. Homework Equations 3. The Attempt at a Solution in the picture thank you 1. Homework Statement 2. Homework Equations 3...
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    Comparison test

    1. Homework Statement Using the limit comparison test to determine convergence or divergence (1) \sum^{\infty}_{n=1} \frac{(ln(n))^{3}}{n^{3}} (2) \sum^{\infty}_{n=1} \frac{1}{\sqrt{n} ln(x)} (3)\sum^{\infty}_{n=1} \frac{(ln(n))^{2}}{n^{\frac{3}{2}}} 2. Homework...
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    Exponential integration

    1. Homework Statement exponential integration formula ∫a^{u} du = \frac {a^{u}}{ln(a)} +c ∫ \left(\frac{2}{3}\right)^{x} dx 2. Homework Equations \frac{}{} 3. The Attempt at a Solution ∫ \left(\frac{2}{3}\right)^{x} dx = \frac{\left(2/3 \right)^{x}}{ln(2)/ln(3)} <<< this is my...
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    Limit of sequence (2)

    1. Homework Statement Find the limit of this sequence An = \frac{n^{n}}{(n+3)^{n+1}} 2. Homework Equations 3. The Attempt at a Solution The answer is 0 but my answer is 1 thank you
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    Find the limit of sequence (trig term)

    1. Homework Statement find the limit of this sequence 1) An = \frac{\sqrt{n} sin (n! e^{n})}{n+1} 2) An = 4n^{3} sin\frac{1}{n^{3}} 2. Homework Equations 3. The Attempt at a Solution (1) |sin n! e^n)| ≤1 |An| ≤ \frac{ \sqrt{n} }{n+1} |An| ≤ \frac{...
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    L' Hopital's rule

    ^{}1. Homework Statement lim _{x\rightarrow\infty} \left(cos\frac{1}{x}\right)^{x} find the limit using L' Hopital's Rule 2. Homework Equations 3. The Attempt at a Solution 1^{\infty} >> change form to 0/0 by taking ln both sides ln(y) = lim _{x\rightarrow\infty} x ln...
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    Solve the integral of differential equation

    1. Homework Statement Solve the integral of differential equation ∫^{t}_{0} y(\tau) d\tau -\acute{y} (t) = t for t≥0 with y(0)=4 3. The Attempt at a Solution take laplace both sides \frac{Y}{s} - sY + 4 = \frac{1}{s^{2}} Y \frac{1 - s^{2}}{s} =\frac{1}{s^{2}} - 4 Y...
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    Unit step functions to find Laplace Transform

    1. Homework Statement f(t) = cos (pi*t) if 1\leq t <4 and 0 elsewhere using unit step functions to find Laplace Transform 2. Homework Equations 3. The Attempt at a Solution I came up with the unit step function f(t) = cos(pi*t) u(t-1) - cos(pi*t) u(t-4) in order to use the second...
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    Inverse laplace transform

    1. Homework Statement find the inverse laplace transformation of \frac{5s+4}{s^2} e^{-2s} 2. Homework Equations 3. The Attempt at a Solution I have tried to partial fractions \frac{5s+4}{s^2} and I got \frac{5}{s}+\frac{4}{s^2} and I know that the answer must have u(t-2) because of...
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