x = 1002 and fl(x) = 1001. Show the relative error is roughly smaller than the condition number times the relative error in x, assuming no round- off error in the computation. (The same examples will show up below and are totally different when round-off error exists. But for this problem, the two questions have same answer. ) 1 (a) f(x) 1 1 (b) f(x): x +1 x(x+1)

Please check my answers

USING PYTHON NOT MATLAB We can use the sum of the first n terms of the Taylor series of e x with a = 0 to estimate the value of the exponential function. Using a logarithmic y axis, plot the fractional error in the estimated e x (compared to numpy.exp(x)) as a function of n (n ranging between 1 and 80) for (a) x = 15 and (b) x = −15. [You can plot the two cases either as different curves on the same plot or in different plots, whichever is clearer.] Discuss the contributions of truncation and roundoff to the fractional error for the different values of x and n. Also discuss how you could reduce truncation and roundoff errors in order to estimate e x more accurately using the Taylor series.

Please do part B-D and make sure the code is in python

A vertical photograph taken from a camera has calibrated focal length f153.206 mm contains an image point "a" of object point A at coordinates x=64.969 mm. y =-78.526 mm relative to the fiducial axes, Calibration sheet shoWS x = 0.247 mm and y= 0.238 mm as calibrated coordinates of principal point. Also, lists the radial lens distortion coefficients K1 2.99778547 x10-08 mm-2 K2-3.15091119 x10A-12 mm-4: K3 H 6.05776623 x10-17 mm-6. Compute the corrected coordinates for the image point "a"

Write a MATLAB function that calculates the approximate value of six(x) using the Maclaurin series approximation from x-0 to xi+1 six(x) = x -+-+. 3 5 The function should accept 3 parameters: value of x, number of significant figures accuracy i.e. n, and the maximum number of iterations. In the function, use ɛ = (0.5 × 10²-" )% in order to continue until the ɛa falls below this criteria. The function should return 3 values: the approximate value of arctan(x) at the end of the program, final ɛg and the number of iterations it took. Submit short snapshots showing the program running.

Please do the following question with the required python coding. Question is in the photo.

Using any CAS or programming language

Suppose that you want to calculate 1434661 · 3785648743 − 100020304 · 54300201. You are told thatthe answer is a positive integer less than 90. Compute the answer mod 10 and mod 9, then combineto get the answer. Show all the necessary work to obtain your answers. Note: This technique hasoften been employed to do calculations with large integers because most of the computations use smallintegers, with only the Chinese Remainder Theorem step requiring large integers. For example, if theanswer is known to be less than 1036, the calculations can be done mod p for each prime less than100. Since the product of the primes less than 100 is approximately 2.3 × 1036, the Chinese RemainderTheorem gives the answer exactly

Q2. Given, F(w,x,y,z) = II M(0,4,8,12) ; (here M means Maxterms) a) Complete the truth table for F W X F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 b) Write the minimum expression of F