1. Use Theorem 7.1.1 to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = 6t5 ℒ{f(t)} =   2. Use Theorem 7.1.1 to find ℒ{f(t)}. (Write your answer as a function of s.) f(t) = et cosh t ℒ{f(t)} =   3. Use Definition 7.1.1, DEFINITION 7.1.1    Laplace Transform Let f be a function defined for  t ≥ 0.  Then the integral ℒ{f(t)} =  ∞ e−stf(t) dt   0is said to be the Laplace transform of f, provided that the integral converges. to find  ℒ{f(t)}.  (Write your answer as a function of s.) f(t) =    cos(t),      0 ≤ t < ? 0,   t ≥ ?ℒ{f(t)} =                          (s > 0)

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.