NEED ANSWERS ASAP PLEASE

1. Compute the absolute error and relative error in approximation of x by x. a) x=,x=22/7 b) x=,x=3.1416. 2. Write the Taylor series for the function f(x)=x32x2+4x1 expanded about x0=2. 3. a) Determine the Taylor series for sinhx=2exex about x0=0. b) Evaluate sinh(1) by using the first three terms of the series. c) Find the absolute error and relative error in approximation sinh(1) assuming you know the value of sinh(1)=2e1c1=1.175201194. 4. Consider integral In=01x+5xndx,n=1,2,,20. a) Estabilish the recursive relation between In and In1 with I0=ln6ln5. Hint: In+5In1 can be calculated explicitly, see lecture notes. b) Establish the recursive relation between error terms errn and errn1. Suppose an error err 0 is introduced initially in the computation of I0. c) How err 0 is amplified at the nth step? Is this algorithm numerical stable