4. [3/4 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 7.6.011. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER A cable that weighs 6 Ib/ft is used to lift 750 lb of coal up a mine shaft 700 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter x * as xj.) lim E 6x; ) Ax n -+00 i =1 X Express the work as an integral and evaluate. 700 750 + 6x )dx = 1995000 ft-lb Need Help? Read It Submit Answer3. [112 Points] DETAILS PREVIOUS ANSWERS SESSCALCZ 8.5.016. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the radius of convergence, R, of the series. i: knew n=0 3n+l R='1 9' Find the interval, 1, of convergence of the series. (Enter your answer using interval notation.) :='{1.1} 3: Need Help? _' 3. [4/6 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 8.6.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) Use differentiation to find a power series representation for f (x ) = (5 + x) 2 f ( x ) = (- 1)nn n+1 52 + n n = 0 What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f ( x ) = (5+ x) 3 . f ( x ) = E ( - 17) an ((1+n) (5+n) ) n = 0 510 +n X What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for x2 f ( x ) = - (5+ x) 3 f ( x ) = (-1)nn (n(n -1) ) n = 2 5 (2+n) X What is the radius of convergence, R? R = 5 Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form a ( b + cx ) 2 ' * you may first find the power series representation of the function b + cx . The resulting power series converges on the same interval. Need Help? Read It Watch It Submit Answer 4. [0/2 Points] DETAILS PREVIOUS ANSWERS SESSCALC2 8.6.015.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a power series representation for the function. f(x) = In(11 - x) f(x) = In(11) +C n = 1 X Determine the radius of convergence, R. R = 1/11 X Need Help? Read It Watch It Master It5. [-/2 Points] DETAILS SESSCALC2 8.6.025.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Evaluate the indefinite integral as a power series. 1 - tli dt C + > What is the radius of convergence R? R = Need Help? Read It Watch It Master It Submit Answer 6. [-/1 Points] DETAILS SESSCALC2 8.6.029. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use a power series to approximate the definite integral, I, to six decimal places. Co.1 Edx 1+ x5 I = Need Help? Read It Watch It Submit Answer 7. [-/2 Points] DETAILS SESSCALC2 8.6.505.XP. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find a power series representation for the function. f(x) = arctan() ( ( x ) = n = 0 Determine the radius of convergence, R. R = Need Help? Read It Submit