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G food cx ← → C = M Gmail YouTube + L Respo X G Gmail x G how to x 308 First Semester Maps News Maps classroom.google.com/u/0/c/NTA2Mzc5ODc0MDE3/m/NTM1MTE1MzQ1NTU4/details Type here to search Translate Respo X O Navba X How TX A Practic X WCSS BX OUsing X 1. Explain what is meant by stability of an algorithm in relations to the Relative Error. 2. What is the difference between the relation error and an absolute error of a given computation problem? | Mi Your X 3. If problem P defined by a with z 5.5, the approximation values for and are denoted by and respectively, what is the condition for P? 4. Recall from calculus that the Taylor series expansion of the exponential function is given by z² 2-3 e = 1+x+ + 21 31 1-0 (a) Can compute an infinite sum computationally without also using infinite resources? Please give an explanation to your answer. (b) Consider the truncated series for the first n terms. 5. Floating Point Numbers and Operations (12.5 Marks) A floating point number system is defined by three components. (1) Is this actually a good or poor algorithm for computing the exponential function? Please give an explanation to your answer. (c) List and explain with example two important primary source of error. (2) With (1.1100) 2 x 2(-01102-0.0274375 in equation 3, what is the relative error? 6. What's the major difference between Tractability and Intractability problems? (a) What are the three components? (b) What is the significant of the combination of the three components? (c) The absolute relative true error in representing a number will be less then the machine. epsilon. Given (0.02832)10, we can say that (0.02832),0 (1.1100)2 x 2-5 (1.1100) × 2(-0110) (3) 7. List four applications of Intractability results. 8. Consider a problem P with input à "which requires the computation of a desired output - A a N Ď # 2 C Get H x | New x | + 30°C Mostly sunny QE ☆ ^540) C DM M ⠀ 12:10 PM 6/29/2022 13