Problem 1 (3 pts): Let f(x) 1+ In( x)/(x - e) Propose a numerically sound algorithm...
Let f(x) = 1 + x − (sin(x)/(x · (e^x) )). Propose a numerically sound algorithm for evaluating f(x) for x ~ 0. Please provide all steps/details, including your thought process so I can follow along and learn, thanks!
which part b uses the answer from part a. 4. (35 pts) Let f(x) = x(1-x) for 0 < x < 1. (a) (15 pts) Compute the Fourier cosine series FCS f(x). (b) (5 pta) Find the formal solution of the problem BC u,(O, t)-u(1,t)-0, (c) (5 pts) Show that there can be no solution of problem (A) which is Ca for 0 S S 1 and (d) (10 pts) Show that there is a Co solution of the DE...
Problem 2 (30 pts) This problem has six parts that may be worked independently. Let X(e) be the Fourier transform of the discrete-time signal x[n] show below. x[n] -7 -5 -3 -2 2 -1 4 5 a) Find X(e). (5 pts) b) Determine ZX(el), the phase of X(e), (5 pts) c) Evaluate )do. (5 pts) Intel® d) Find X(el). (5 pts) e) Determine and sketch the signal whose Fourier transform is ReX(0)} (5 pts) f) Evaluate xo do. (5 pts)...
please show work 1.Let g(x) = log3(x +3)-1 . d. (3 pts) f(8)-3, the corresponding point on the graph of f(x)is.H The transformed point on the graph of g(x) is . e. (2 pts) Find the domain and the range. Write in interval notation. 1d. point on f(x): point on g(x): f. (1 pt) What is the vertical asymptote? That is, as x→ 1e. D: R: 1f. 8. (5 pts) Find the equation of the inverse, g(x). 1g. 1.Let g(x)...
(6 pts) Let f(x) = (x2 + 3x + 1)e-x. (a) (1 pt) Find f'(2) (b) (3 pts) Solve for the intervals of increase and decrease. Show your work. (c) (2 pts) Find any local maxima or minima, and where they occur.
4. (30 pts) Let (X,Y) have joint pdf given by < , | e-9, 0 < x < f(x,y) = 3 | 0, 0.w., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
Problem # 1: Let 3-1x< . f(x) 7x 0 x1 The Fourier series for f(x). (an cosx bsinx f(x) n1 is of the form f(x)Co (g1(n,x) + g2(n, x) ) n-1 (a) Find the value of co. (b) Find the function gi(n,x) (c) Find the function g(n, x) Problem #2 : Let f (x ) = 8-9x, - x< I Using the same notation as n Problem #1 above, (a) find the value of co- (b) find the function g1(n,x)....
Q 5. Let F be a field and consider the polynomial ring l (a) State the Division Algorithm for polynomials in Plrl. b) Let a e F. Prove that -a divides f(x) in Fix] if and only if (a)- (c) Prove that z-37 divides 42-1 in F43[z]. Q 5. Let F be a field and consider the polynomial ring l (a) State the Division Algorithm for polynomials in Plrl. b) Let a e F. Prove that -a divides f(x) in...
Let (X, d) be a metric space, and let ACX be a subset (a) (3 pts) Let x E X. Write the definition of d(x, A) (b) (7 pts) Assume A is closed. Prove that d(x,A-0 if and only if x E A. Let (X, d) be a metric space, and let ACX be a subset (a) (3 pts) Let x E X. Write the definition of d(x, A) (b) (7 pts) Assume A is closed. Prove that d(x,A-0 if...
4. Let X have pdf f (x) as follows f(x) = 1.8 1(0 1/21+ .21(1/2 < x 1) x (8 pts) What is E[X]? Justify your answer. . (12 pts) Write Matlab or pseudocode that will produce 10, 000 PRNG samples with the dis- tribution of X. Have the output recorded in the vector a (i.e., so that ar(1) is the first sample, r(2) is the second sample, etc.) 4. Let X have pdf f (x) as follows f(x) =...