Expand g (a) = e 7 in powers of (a + 1). O (-1)*e77*(x + 1)k k! O D (-1)e(x + 1)k k! O (-1)ke(x +1)k k! O (-1)*-17k(x+ 1)k k! O M 8 (-1)kle77kti(x + 1) k!Question number 7. Assume that f(x) = In(1 + a) is the given function and that P, represents the nth Taylor Polynomial centered at a = 0. Find the least integer n for which Pr (0.9) approximates In (1.9) to within 0.001. O 32 O 36 O 35 O 30 O 34Use a Tay'or polynomial centered at x : 0 to estimate 1n{1.55) to within 0.01. if: n 451 O u 441 O 0 431 O 0421 O 0411 Question number 9. Given the function f(x) =x3 sin ( ), find f() (0) . (Hint: Write the Taylor series of the given function.) O -15 O -120 O -960 O 48 O O None of the above. Question number