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second derivative of e to the X is and
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second derivative of e to the X is and
so on because that comes into the Taylor
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so on because that comes into the Taylor
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so on because that comes into the Taylor
formula for the for the coefficients but
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formula for the for the coefficients but
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formula for the for the coefficients but
we know what the derivative of e to X is
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we know what the derivative of e to X is
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we know what the derivative of e to X is
it's just e to the X again and it's that
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it's just e to the X again and it's that
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it's just e to the X again and it's that
way all the way down all the derivatives
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way all the way down all the derivatives
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way all the way down all the derivatives
are e to the x over and over again so
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are e to the x over and over again so
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are e to the x over and over again so
when I evaluate this at x equals 0 well
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when I evaluate this at x equals 0 well
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when I evaluate this at x equals 0 well
the value of e to the X is 1 the value
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the value of e to the X is 1 the value
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the value of e to the X is 1 the value
of e to the X is 1 and x equals 0 you
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of e to the X is 1 and x equals 0 you
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of e to the X is 1 and x equals 0 you
get a value of 1 all the way down so all
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get a value of 1 all the way down so all
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get a value of 1 all the way down so all
these derivatives at 0 have the value 1
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these derivatives at 0 have the value 1
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these derivatives at 0 have the value 1
and
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and
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