4s +1 Consider the function F(s)= s3 - 3s2 + 3s - 1 a. Find the partial fraction decomposition of F(s): 4s + 1 + s3 - 3s2 + 3s – 1 b. Find the inverse Laplace transform of F(s). f(t) = L{F(s)} = %3D

Find the degree three Taylor polynomial T3 centered at x = = 0 for f when 2. T3(x) 1. T3(x) = ln 3. 3. T3(x) 4. T3(x) 5. T3(x) f(x) 6. T3(x) = - X 3 = = = = In 3+ 4 3x = In 3 4 -X 3 + ln(3 – 4x). 4 -X 3 x² 4 8 io - X 3 9 22 - 9 + 8 9 64 81 + 8 610 شرح 4 z x + 7 x 64 81 X3 + 64 81 خرج 64 -x³ 81 32 -x³ 81 64 من مخ 81

Find a second degree polynomial P such that P(2) = 7, P'(2)=5, and P'"(2) = 2. %3D •.