Question Solved1 Answer My question is number 18.Thank you! In Exercises 15 through 20, write a formula for the nth term of the sequence. Identify your formula as recursive or explicit. 15. 1, 3, 5, 7, ... 16. 0, 3, 8, 15, 24, 35, ... 17. 1, -1, 1, -1, 1, -1, ... 18. 0, 2,0, 2, 0, 2, ...

Let R be the region enclose by the graphs of y=lnx, the line x=3, and the x-axis. Set up, but do not integrate, an integral expression in terms of a single variable for the volume solid generated by revolving R about the line x=3

Question 1 1 pts Consider the task of sketching G, given a graph of its derivative function g, and the information that G (2) = 1. • At x-values where g is positive, G should be (Select] • At x-values where g is increasing, G should be (Select] • Any value of G (the [Select] of its graph) can be determined by the formula G (x) = 1+ S7 g(t) dt. Question 2 1 pts How many antiderivatives does a given function have? (Select] What do they all have in common? (Select] Question 3 1 pts Active Calculus states: The rule A (2) = Si f(t) dt defines a new function that measures the [Select] bounded by f on any interval [a, x] We call the function A the integral function corresponding to f. Question 1 Consider the task of sketching G, given a graph of its derivative function g, and the information that G (2) = 1. • At x-values where gis positive, G should bv [ Select ] concave up • At x-values where g is increasing, G should increasing positive • Any value of G (the [ [ Select] of its graph) can be determined by the formula G (x) = 1 + $z* g(t Question 1 Consider the task of sketching G, given a graph of its derivative function g, and the information that G (2) = 1. O At x-values where g is positive, G should be [Select] O At x-values where gis increasing, G should be [Select] 0 of its graph) can be determined by the formula G (x) = 1 + $26 g(t) Any value of G (th [ Select ] slope net signed area height Question 2 How many antiderivatives does a given function have v [ Select ] 2 infinitely many What do they all have in common? [Select] about 100 Question 2 How many antiderivatives does a given function have? [Select] What do they all have in common [ Select ] They differ by a constant (a vertical shift). They have the same absolute value Question 3 Active Calculus states: bounded by fon any inte The rule A (x) = Sa f (t) dt defines a new function that measures th V[ Select ] slope [a, x]. derivative net signed area We call the function A the integral function corresponding to f. velocity

4. A smooth horizontal circular wire of radius R is forced to rotate at a fixed angular velocity w about a vertical axis through the pivot point located on a circle. A bead of mass m is threaded on the wire and is free to move around it without friction. Specify position of the bead on the wire by the angle y that it makes at the center with the diameter passing through the pivot point and the center so that when the bead is on the opposite side of the diameter from the pivot point the y = 0. (a) Find the Lagrangian for this system using Y as the generalized coordinate. (b) Derive Euler-Lagrange equation of the bead motion. (c) Determine integrals of motion of this system (d) Find frequency of small oscillations (y <) around y = 0 and the solution which corresponds to initial conditions plezo = Po and pleo = Po (e) [Extra Credit] Find the period of oscillations numerically for initial conditions ele-o = 1 and 4–0 = 0. Hint: Numerical value of the integral los videos dr ivarº (+) = 2.622 1 may be useful.

Problem 7.35 (page 287) "Figure 7.16 is a bird's-eye view ..." [6 points] Hint: In this problem the potential energy U is zero, so that there is only kinetic energy T. 7.35** Figure 7.16 is a bird's-eye view of a smooth horizontal wire hoop that is forced to rotate at a fixed angular velocity w about a vertical axis through the point A. A bead of mass m is threaded on the hoop and is free to move around it, with its position specified by the angle o that it makes at the center with the diameter AB. Find the Lagrangian for this system using o as your generalized coordinate. (Read the hint in Problem 7.29.) Use the Lagrange equation of motion to show that the bead oscillates about the point B exactly like a simple pendulum. What is the frequency of these oscillations if their amplitude is small?

A graphing calculator is recommended.The Gateway Arch in St. Louis was designed by Eero Saarinen and was constructed using the equationy = 211.49 − 20.96 cosh(0.03291765x)for the central curve of the arch, where x and y are in meters and |x| ≤ 91.20. a-What is the height (in m) of the arch at its center? (Round your answer to two decimal places.) b-At what points is the height 50 m? (Round your answers to two decimal places.)smaller x-value (x, y)=larger x-value (x, y)= c-What is the slope of the arch at the points in part b? (Round your answers to one decimal place.)at the point with smaller x-value     at the point with larger x-value     

options: increasing, positive, concave upnet signed area, slope, height1. slope, distance traveled, displacement2. make negative contribution, should be disregarded, countexactly the same as regions above the horizontal axis3. position, total distance traveled, displacement4. odd and even, increasing and decreasing, forward moving andbackward moving Sorry I asked this question like 4 times and no one answered it): Consider the task of sketching G, based two pieces of given information: 1. a graph of its derivative function g, and 2. the information that G (2) = 1. . At x-values where g is positive, G should be increasing • At x-values where g is increasing, G should be positive . Any value of G can be determined by the formula G(X) = 1+Sg(t) dt. This formula will tell us the net signed area of the G graph at a given x- value. Question 3 Active Calculus states: bounded by on any inte The rule A (x) = f(t) dt defines a new function that measures the [ Select] slope derivative We call the function A the integral function corresponding to f. net signed area velocity