HW 04: Difference between revisions
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(New page: <math>\underbrace{10 [u(t-2) - u(t-3)]}_{x(t)} * \underbrace{e^{-t}u(t)}_{h(t)}</math>) |
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<math>\ |
Find <math>\overbrace{10 [u(t-2) - u(t-3)]}^{x(t)} * \overbrace{e^{-t}u(t)}^{h(t)}</math> |
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[[Image:HW04.PNG]] |
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<math>10 [u(t-2) - u(t-3)] * e^{-t}u(t) = |
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\begin{cases} |
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0, & t \le 2 \\ |
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\int_{t-3}^{t-2} 10 \cdot e^{-\lambda} \,d\lambda, & t > 2\\ |
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\end{cases} = \begin{cases} |
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0, & t \le 2 \\ |
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10\,e^{3-t}-10\,e^{2-t}, & t > 2\\ |
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\end{cases} |
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</math> |
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Latest revision as of 13:13, 17 November 2008
Find
![{\displaystyle \overbrace {10[u(t-2)-u(t-3)]} ^{x(t)}*\overbrace {e^{-t}u(t)} ^{h(t)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/138aa913f26a9ea9e91bac08f8a2ac3df40a3e34)
![{\displaystyle 10[u(t-2)-u(t-3)]*e^{-t}u(t)={\begin{cases}0,&t\leq 2\\\int _{t-3}^{t-2}10\cdot e^{-\lambda }\,d\lambda ,&t>2\\\end{cases}}={\begin{cases}0,&t\leq 2\\10\,e^{3-t}-10\,e^{2-t},&t>2\\\end{cases}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b415c7531b6397061ff2aed57ee27f4e72779c95)