.. Finl sample . Help please

1. Find the Riemann sum for the function /(x) = sin(x) on the interval 0, by using four equal subintervals and the left endpoints of each subinterval as the sample points. 2. Express the integral 1 rl + 1 dex as a limit of the Riemann sum using n subintervals of equal length and right endpoints as sample points. (a) > 1 310 (6+4)+1 (b) lim +1 (c) 31 1-1 + 1 (d) lim (2+30)1 (c) lim Li 1+1 3. Find the derivative of the function sin(x) F(x) = sect dt. 1. Evaluate the definite integral VI(x + 1) dr. 5. A particle is moving and has acceleration given by a(t) = - sin(t). The initial velocity is v(0) = 2 and the initial position is s(0) = -3. Find the position of the particle at time f. 6. Let R(t) be the rate, in gallons per hour, at which oil leaks out of a tanker f hours after an accident. Which of the following expressions gives the total amount of oil that leaks out in the first 10 hours after the accident? (a) R(10) (b) R(10) - R(0) (c) R(10) - R(0) 10Math 140 - Exam 7 (Final) Practice Problems (d) R(t) dt (e) R(10) - R(0) 7. Use a Riemann sum to estimate dr using three subintervals of equal length and right endpoints as sample points. 142 105 96 49 24 7 11 15 8. Express the integral V2 + I de as a limit of the Ricmann sum using n subin- tervals of equal length and right endpoints as sample points. 1-+00 (a) lim > (2) 2 + (24)" (b) lim > (3) V/2+ (1+ 2) (c) lim 1=1 1-+00 (d) lim > (1) 3 + (:) (e) lim * ( 2 ) / 2 + ( 1 + 21 )" 9. Suppose that f(x) dx - 5. Find (25 + 35(x)) dx. 10. Find the derivative, F(x), of F(x) = / v10+ + di. 11. Evaluate the integral S' + +1