ECE 202 Lesson 19 - 29 29 29 29 29 29 29 lim lim lim lim...

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ECE 202 Circuit Theory 2 Lesson 19 Final-Value Theorem Initial-Value Theorem
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2 Limit of the Laplace Transform of a Derivative as s Approaches Zero ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 0 0 0 0 lim lim lim 0 st st s st s t g t f t G s f t e dt f t e dt f t dt f t f t e dt f t f t - - - - - - - - = = = = = - - °
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3 Limit of the Laplace Transform of a Derivative as s Approaches Zero ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 0 0 lim lim 0 st st s s g t f t G s f t e dt G s sF s f f t e dt sF s f t - - - - = = = - - = - -
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4 Final-Value Theorem ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 0 0 0 lim lim 0 lim lim 0 lim lim st s t st s s t s f t e dt f t f f t e dt sF s f f t sF s t - - - - = - - = - - = from slide 2 from slide 3 final-value theorem
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5 Limit of the Laplace Transform of a Derivative as s Approaches Infinity ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 0 0 0 0 0 0 0 0 0 st st st st g t f t G s f t e dt G s f t e dt f t e dt f t e dt f t dt f t f f t - - + - - - + + + + - - - - = = = + = = = + - - no impulse function at the origin
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6 Limit of the Laplace Transform of a Derivative as s Approaches Infinity ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 0 0 lim 0 0 lim 0 lim lim lim 0 lim 0 lim 0 0 st st st s s st
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Unformatted text preview: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 lim lim lim lim lim 0 lim lim st st st s s st t j t j t s s s s s G s f t e dt f t e dt G s f f f t e dt e e e e G s f f σ ϖ +---+-+----Υ ℑ = + = + -- + = = = = + --& 7 Limit of the Laplace Transform of a Derivative as s Approaches Infinity ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 lim lim st s s g t f t G s f t e dt G s sF s f G s sF s f t--= = =--=--8 Initial-Value Theorem ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 lim lim lim lim lim lim s s s s t s G s f f G s sF s f f sF s f t sF s t t t t = + --=--+ = = from slide 6 from slide 7 initial-value theorem...
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