Sagittarius A-Star's latest activity
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.you're welcome -
Sagittarius A-Star reacted to Mike_bb's post in the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##? with
Like.
Sagittarius A-Star Big thanks!!! I appreciate you very much! Now I understand how it works! -
Sagittarius A-Star reacted to Mike_bb's post in the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##? with
Agree.
Sagittarius A-Star In your proof you use the fact that ##exp(x)'=exp(x)##, right? -
Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.If you put ##10^y## as upper limit, then you would get ##F'(y)=\frac{1}{10^y}\cdot {d \over dy}(10^y) \neq 1## and ##F(y) \neq y##.
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.Please see above in posting #13.
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.In Wolfram Alpha they write ##log()## for the natural logarithm, which is usually written as ##ln()##. They mention it:
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.The simplification in posting #6 goes: ##F'(y)=\frac{1}{e^y}\cdot {d \over dy}(e^y) = 1##.
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.That's not true. Proof: https://www.wolframalpha.com/input?i2d=true&i=Integrate%5BDivide%5B1%2Ct%5D%2C%7Bt%2C1%2CPower%5B10%2Cy%5D%7D%5D
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.Then you would not get ##F(y) = y## after integrating.
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.According to the chain rule: ##F'(y)=\frac{1}{e^y}\cdot {d \over dy}(e^y)## Maybe you continue the calculation first for ##e## and then...
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.I think you will see the answer after the calculation (chain rule).
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Sagittarius A-Star replied to the thread Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?.You may differentiate the function ##F(y)=\int_1^{e^y}\frac{1}{t}\,dt## without using the ##ln(x)## function, simplify ##F'(y)## and...
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Sagittarius A-Star replied to the thread Undergrad Ampère's mercury experiment and Aharonov-Bohm: same message?.The displacement current does not contribute directly to the x-components of the forces on the charged spheres.
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Sagittarius A-Star replied to the thread Space Stuff and Launch Info.Today, the European Space Agency (ESA) launched an Ariane 64 (variant with 4 instead of 2 boosters) to bring 36 satellites into low...
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Russia will decommission the PrK ISS module which keeps leaking. It will be depressurized. It was used for Progress resupply vehicles...
