Number 4 please it's on the bottom of the left page and the rest of the problem cuts to the top of the right page.

O during the time interval [a, b] is approximately right endpoints. Sketch the graph and the rectangles, Is your estimate an underestimate or an overestimate? (to ) Ar + 5 ( 1 ) A1 + . . . + 5 ( 1-1) At - ES( tix ) At (b) Repeat part (a) using left endpoints. clocity at right endpoints instead of left endpoints, our estimate for the 5. (a) Estimate the area under the graph of f(x) = 1 + x from * - - 1 to x - 2 using three rectangles and right comes endpoints. Then improve your estimate by using six rectangles. Sketch the curve and the approximationg rectangles . ently we measure the velocity, the more accurate our estimate (b) Repeat part (a) using left endpoints. ems plausible that the exact distance d traveled is the limit of such (c) Repeat part (a) using midpoints. (d) From your sketches in parts (a) (c), which appears to be the best estimate? d = lim .f(t-1) Ar = lim Ef(t,) At A9 6. (a) Graph the function f ( x ) = 1/ ( 1 + * 2 ) - 25 x 52 tion 4.3 that this is indeed true. on 3 has the same form as our expressions for area in Equations 2 (b) Estimate the area under the graph of f using four nat the distance traveled is equal to the area under the graph of approximationg rectangles and taking the sample po on. In Chapter 7 we will see that other quantities of interest in the to be (i) right endpoints and (ii) mi (ii) midpoints. In each fences-such as the work done by a variable force-can also be case sketch the curve and the rectangles . ca under a curve. So when we compute areas in this chapter, bear (c) Improve your estimates in part (b) by using eight rectangles. n be interpreted in a variety of practical ways. 7. Evaluate the upper and lower sums for f(x) = 2+ 0