# Scientific Computing I-APPROXIMATIONS AND ROUND-OFF ERRORS

1.Evaluate e power?5 using two approaches e power?x=1x+xpower2/2?xpower3/3!+ and epower?x=1/e power x=1/(1+x+(xpower2/2)+(xpower3/3!))+ and compare with the true value of 6.737947×10power?3. Use 20 terms to evaluate each series and compute true and approximate relative errors as terms are added. 2.The derivative of f(x)=1/(1-3x power2) is given by 6x/(1=3x power 2)whole power2 Do you expect to have difficulties evaluating this function at x = 0.577? Try it using 3- and 4-digit arithmetic with chopping. 3.(a)Evaluate the polynomial y=xpower 3-5xpower2+6x+0.55 at x = 1.37. Use 3-digit arithmetic with chopping. Evaluate thepercent relative error. (b)Repeat(a) but express y as y=((x-5)x+6)x=0.55 Evaluate the error and compare with part(a). 4.Use 5-digit arithmetic with chopping to determine the roots of the following equation with Eqs. (3.12) and (3.13) xpower2-5000.002x+10 Compute percent relative errors for your results. 5.The divide and average method, an old-time method for approximating the square root of any positive number a , can be formulated as x=(x+(a/x))/2 Write a well-structured function to implement this algorithm basedon the algorithm outlined in Fig. 3.3

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