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62 Solution of initial value problems (4) Topics † Properties of Laplace transform, with proofs and examples † Inverse Laplace transform, with examples, review of partial fraction, † Solution of initial value problems, with examples covering various cases Properties of Laplace transform 1 Linearity Lfc1f(t)c2g(t)g = c1Lff(t)gc2Lfg(t)g 2 First derivative Lff0(t)g = sLff(t)g¡f(0)Math131 Calculus I The Limit Laws Notes 23 I The Limit Laws Assumptions c is a constant and f x lim ( ) →x a and g x lim ( ) →x a exist Direct Substitution Property If f is a polynomial or rational function and a is in the domain of f, then = f x lim ( ) x aUnit 3 Algebra 1; The Ramanujan Summation 1 2 3 1 12 By Mark Dodds Cantor S Paradise Medium 1+2+3+4+5 to infinity=-1/12 proof pdf