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Calculus/Exponentials

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Expert: Scotto - 6/22/2008


Question
Mathematical proof of f(0) = 1 where f(x)= a^x.

Answer
x^n means take 1 and multiply it by x for a total of n times.

Since x, the number times it is multiplied is 0, the answer starts as 1 and stops as 1.

Consider all numbers raised to the 0.  The function is then a^x where x is zero and a can vary.  Take the derivative and you get xa^(x-1).  Since x is 0, this makes the entire derivative 0.  This means the function has no slope and is a constant for all a.

If you take a number, say 2, and let the power approach zero, you get close to 2.  That looks like and epsilon-delta proof, if you've heard of those.  Take any epslion close to 1, and you can get a delta so that if the power is smaller than delta, then how far from the number you are is less than epsilon.

This can also be tried on any calculator.  Take any number a and put it to the 0 power.  You get 1.

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Scotto

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Any kind of calculus question you want. I also have answered some questions in Physics (mass, momentum, falling bodies), Chemistry (charge, reactions, symbols, molecules), and Biology.

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Experience in the area: I have tutored students in all areas of mathematics for over 25 years. Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors. Awards and Honors: I have passed Actuarial tests 100, 110, and 135.

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Maybe not a publication, but I have respond to well oveer 7,500 questions on the PC. Well over 2,000 of them have been in calculus.

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I aquired well over 40 hours of upper division courses. This was well over the number that were required. I graduated with honors in both my BS and MS degree from Oregon State University. I was allowed to jump into a few junior level courses my sophomore year.

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I have been nominated as the expert of the month several times. All of my scores right now are at least a 9.8 average (out of 10).

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My past clients have been students at OSU, students at the college in South Seattle, referals from a company, friends and aquantenances, people from my church, and people like you from all over the world.

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