1.Evaluatee power−5using two approachese power−x=1–x+xpower2/2−xpower3/3!+……andepower−x=1/e power x=1/(1+x+(xpower2/2)+(xpower3/3!))+……and compare with the true value of6.737947×10power−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 by6x/(1=3x power 2)whole power2Do 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 polynomialy=xpower 3-5xpower2+6x+0.55at x =1.37. Use 3-digit arithmetic with chopping. Evaluate thepercent relative error.(b)Repeat(a) but express y asy=((x-5)x+6)x=0.55Evaluate 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+10Compute percent relative errors for your results.5.The “divide and average” method, an old-time method for approximating the square root of any positive numbera, can be formulated as x=(x+(a/x))/2Write a well-structured function to implement this algorithm basedon the algorithm outlined in Fig. 3.3
