8 questions

Let F(x) = sin(2t2) at. Find the MacLaurin polynomial of degree 7 for F(x). Use this polynomial to estimate, to 4 decimal places, the value of sin (2x2) dx. Let F(x) = [ e-2 at. Find the MacLaurin polynomial of degree 5 for F(x). C0.17 Use this polynomial to estimate to 4 decimal places the value of e 2x dx. Let F(x) = +3e- 5to dt. Find the MacLaurin polynomial of degree 12 for F(x). T12 = Use this polynomial to estimate (to 5 decimal places) the value of 3e-s' at. This is one you can do analytically (by hand) using the u-substitution u = -5t, Perform the integration and compare with your MacLaurin series approximation. LyJ U/ 1 pt 9 20 Consider the differential equation y"-2xy' ty = 0 subject to y(0) = 1 and y'(0) = 5. The first few terms of the power series solution are y ~ 1+52 - You throw a ball (from ground level) of mass 1 kilogram upward with a velocity of vo = 30 " on Mars, where the force (acceleration) of gravity is Use this to approximate y(x) at x = 0.1 9 = -3.711 m Round your answer to 2 decimal places. A. Approximate, to two decimal places, how long will the ball be in the air on Mars? Question Help: Video Written Example A seconds Submit Question B. Approximate, to two decimal places, how high the ball will go? To test this series for convergence meters Enter an integer or decimal number more.. n Question Help: [ Vidan ... . n=1 Vn' + 1 You could use the Limit Comparison Test, comparing it to the series )1 net np where p = Solve the following initial value problems: dy dt = 8t A. y(0) = 5 : y= B. y(0) = - 3: y= GO/1 pt Solve the initial value problem. y"= 2 + sin(2x), y(0) = -3, y'(0) = -4, y"(0) = 3 y = Question Help: Vidan P w