Consider the function (x) = x - 2x-5 What is (-1)? What is r(5) ? What...
(1 point) - 2x² Find the Maclaurin series for the function f(x) = r the function (x) = - 2 in the form (f(x) = n=0 Notice if a coefficient requested below is missing in the series then that coefficient is zero and you should enter 0. Find the individual coefficients Now give the general term as a formula involving n C. =
answer should be 2x 5. Let X andY joint density function if 0r< 1; 0 <y<r 8.ry f(r,y) = 0 elsewhere. What is the regression curve y on r, that is, E (Y/X = r)?
Find f'(x) and (c) Function Value of c R(x) = (x + 2x)(2x + 2x - 2) c=0 x) (8x3+2)(x4 + 2x) + (2x4 + 2x - 2)(4x3 + 2)
What is the domain?Explain Consider the rational function: x' – 2x² – 16x +32 x* +2x – 13x² -14x +24. R(x) =-
Consider the problem of maximizing the function f(x,y)=2x+3y subject to vx +Jy=5 What should be verified first in order to determine if f has a minimum or maximum 8) Consider the problem of maximizing the function f(x,y)=2x+3y subject to vx +Jy=5 What should be verified first in order to determine if f has a minimum or maximum 8)
Consider the following function. 5 (7) = rsin (2x), a = 0, n = 4,-0.5 5:50.5 (a) Approximate f by a Taylor polynomial with degreen at the number a. 4 4 2x Talx) 3 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) when x lles in the given interval. (Round the answer to four decimal places.) IRA(X)IS
5. (12 pts.) Consider the region bounded by f(x) 4-2x and the x-axis on interval [-1, 4] Follow the steps to state the right Riemann Sum of the function f with n equal-length subintervals on [-, 4] (5 pts.) a. Xk= f(xa) (Substitute x into f and simplify.) Complete the right Riemann Sum (do not evaluate or simplify): -2 b. (1 pt.) lim R calculates NET AREA or TOTAL AREA. (Circle your choice.) Using the graph, shade the region bounded...
. Consider the function f(x) = 2x^ 3 + 9x^ 2 − 24x + 1. (1) (5 points) Find all the critical points of f(x). (2) (5 points) Find the intervals on which f(x) is increasing and decreasing, and find the x-values of any relative minima/maxima.
Consider the following function. f(x) = 5 sinh (3r). a = 0, n=5,-0.3<r <0.3 (a) Approximate f by a Taylor polynomial with degree n at the number a. 3 45x 2 81 5 T5(x) = | 15x + + -X 8 (b) Use Taylor's Inequality to estimate the accuracy of the approximation f = 7,(x) when x lies in the given interval. (Round the answer to four decimal places.) |R5(x)] = 5.19674 X
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks 3. Consider the function defined by...