Question

2.[12 marks] The following problems cellation error. are about roundoff error - Can- Determine a way how to compute the following functions more accu- rately, i.e., how one can avoid cancellation error effectively. (1). 14 marks] fi(x) = x - Vx - 3 when x is large (2). [4 marks] f2(x) = 2 (1 - cos x) when r is near 0. (3). /4 marks] When one applies the quadratic formula 4ac -b+ Vb -4ac -b- 2a 2a 0, where b

Answer 1

ANSToundoff enroy Cancellation oror - up) at just take the limit af these Juretion to find ths moximum Jimit of Junchian when the variable i Jarge too ar too Smalt fix) zlarge Cuhen ay uming im fi (z) Lim Jx23 X - Without imit the JAmcHan iaill be come oo -1 Lim Iim (x3) X lim 1- Put x=00 2(x2 s) - 1 2) 2 (1- Whan x is -cosx near o puting fea) 2 (1-1) 0 O tinding dimit im fatx) Qin 2 (1-casx) Vim 2-20s Oim 2+2Sinx ズニ0 noD puting Dim f(x)- 2 +o 0