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Maclaurin Series
Before working any illustrations of Taylor Series the first requirement is to address the assumption that a Taylor Series will in fact exist for a specified function. Let us start out with a few notation and definitions that we'll require.
To find out a condition that must be true in order for a Taylor series to exist for a function let's first describe the nth degree Taylor polynomial of f (x) as,
.
Note: This actually is a polynomial of degree at most n! If we were to write out the sum with no the summation notation this would obviously be an nth degree polynomial.
Strategy for Series Now that we have got all of our tests out of the way it's time to think regarding to the organizing all of them into a general set of strategy to help us
Theorem, from Definition of Derivative If f(x) is differentiable at x = a then f(x) is continuous at x =a. Proof : Since f(x) is differentiable at x = a we know, f'(a
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School run known to possess normal distribution with mean 440 sec & SD 60 sec. What is probability that randomly chosen boy can run this race in 302 sec.
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Rationalize the denominator for following. Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica
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