1. [1!2 Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 8.7.006. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the Maclaurin series for x) using the definition of a Maclaurin series. [Assume that f has a power series expansion. Do not show that RUM) 0.] rm = e5X rm= 2 le? x\" n=0 ' x Find the associated radius of convergence R. R='OO xi Need Help? 3. [3/4 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 8.7.037. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the Maclaurin series of f (by any method). f(x) = cos(x3) In on f ( x ) = n = 0 (2n) ! X Find its radius of convergence R. R = DO Graph f and its first few Taylor polynomials on the same screen. 1.5 1.5 1.0 1.0 0.5 0.5 $1.0 -0.5 0.5 1.0 -1.0 0.5 0.5 1.0 -0.5 -0.5 1:0 -1.0 O -1.5 O -1.5 1.5 1.5 1:0 1.0 0.5 0.5 -1.0 -0.5 0.5 1.0 -1.0 -0.5 0.5 1.0 -0.5 - 0.5 -1.0 -1.0 -1.5 O -1.5 What do you notice about the relationship between these polynomials and f? As n increases ", Tn(x) becomes a better approximation to f(x). Need Help? Read It Submit Answer 4. [0/1 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 8.7.045. MY NOTES ASK YOUR TEACHER Evaluate the indefinite integral as an infinite series. cos x - 1 dx x In(x) C n = Need Help? Read It Watch It Viewing Saved Work Revert to Last Response Submit Answer6. [2!3 Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 10.1.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Write the equation of the sphere in standard form. x2+y2+22+4x6y4z=1 '[xh]2+(yk]2+(zl)2=n2' X Find its center and radius. 2=3,2 l" ) radius '4 l v Need Help? center (X, y, z) = ( Submit Answer 7. [OH Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 10.1.018.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of a sphere if one of its diameters has endpoints (3, 5, 4) and (5, ?, 8). x2+y2+228x12y 122:82 Need Help? _'_' X Submit Answer 5. [1/2 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 10.2.027. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A woman walks due west on the deck of a ship at 3 mi/h. The ship is moving north at a speed of 18 mi/h. Find the speed and direction of the woman relative to the surface of the water. (Round your answers to one decimal place.) speed 18.24 mi/h direction N 9 X ow Need Help? Read It Watch It Submit Answer 6. [1/3 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 10.2.034. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) Find the unit vectors that are parallel to the tangent line to the curve y = 8 sin x at the point (7/6, 4). (Enter your answer as a comma-separated list of vectors. 7 (i +4V31), - 4(i+4/3;) (b) Find the unit vectors that are perpendicular to the tangent line. 7 (c) Sketch the curve y = 8 sin x and the vectors in parts (a) and (b), all starting at (7/6, 4). y 10 10 - X -5 5 -5 5 -5 -5 O O 10 - X - X -5 5 -5 -5/ -51 O Need Help? Read It Submit Answer2. [1!2 Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 10.3.016. ASK YOUR TEACHER PRACTICE ANOTHER Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) a = (1, o, 2), b = (2, 4, o) exact 78.463 I X approximate T3 I Need Help? Submit