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1. 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
2. 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
3. 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
4. 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
5. 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
6. 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...
7. 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...
8. 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}
9. 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...
10. 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...
11. 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...
12. 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
13. 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{...
14. 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...
15. 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...
16. 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...
17. 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...