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Four friends have been doing really well in their calculus class: they have been getting top grades for their homework and on the midterm. So, when it's time for the final, they decide not to study on the weekend before, but to drive to another friend's birthday party in another city - even though the exam is scheduled for Monday morning. As it happens, they drink too much at the party, and on Monday morning, they are all hung over and oversleep. When they finally arrive on campus, the exam is already over.
They go to the professor's office and offer him an explanation: "We went to our friend's birthday party, and when we were driving back home very early on Monday morning, we suddenly had a flat tire. We had no spare one, and since we were driving on back roads, it took hours until we got help."
The professor nods sympathetically and says: "I see that it was not your fault. I will allow you to make up for the missed exam tomorrow morning."
When they arrive early on Tuesday morning, the students are put by the professor in a large lecture hall and are seated so far apart from each other that, even if they tried, they had no chance to cheat. The exam booklets are already in place, and confidently, the students start writing.
The first question - five points out of one hundred - is a simple exercise in integration, and all four finish it within ten minutes.
When the first of them has completed the problem, he turns over the page of the exam booklet and reads on the next one:
Problem 2 (95 points out of 100): Which tire went flat?
A mathematician went insane and believed that he was the differentiation operator. His friends had him placed in a mental hospital until he got better. All day he would go around frightening the other patients by staring at them and saying "I differentiate you!"
One day he met a new patient; and true to form he stared at him and said "I differentiate you!", but for once, his victim's expression didn't change.
Surprised, the mathematician marshalled his energies, stared fiercely at the new patient and said loudly "I differentiate you!", but still the other man had no reaction. Finally, in frustration, the mathematician screamed out "I DIFFERENTIATE YOU!"
The new patient calmly looked up and said, "You can differentiate me all you like: I'm e to the x."
More advanced story:
A constant function and ex are walking on Broadway. Then suddenly the constant function sees a differential operator approaching and runs away. So ex follows him and asks why the hurry. "Well, you see, there's this differential operator coming this way, and when we meet, he'll differentiate me and nothing will be left of me...!" "Ah," says ex, "he won't bother ME, I'm e to the x!" and he walks on. Of course he meets the differential operator after a short distance.
ex: "Hi, I'm ex"
diff.op.: "Hi, I'm d/dy"
A different version:
The functions are sitting in a bar, chatting (how fast they go to zero at infinity etc.). Suddenly, one cries "Beware! Derivation is coming!"
All immediately hide themselves under the tables, only the exponential sits calmly on the chair.
The derivation comes in, sees a function and says "Hey, you don't fear me?"
"No, I am e to the x", says the exponential self-confidently.
"Well" replies the derivation "but who says I differentiate along x?"
There's a big calculus party, and all the functions are invited. ln(x) is talking to some trig functions, when he sees his friend ex sulking in a corner.
ln(x): "What's wrong ex?"
ex: "I'm so lonely!"
ln(x): "Well, you should go integrate yourself into the crowd!"
ex looks up and cries, "It won't make a difference!"
Contributed by Erik via feedback