Nikita Sharma 2019W2MATH101209 Assignment Homework1 due 9/12/14 at 9pm 1.(1 point) (a) Estimate the area under the graph off(x) =3=xfrom x=1 tox=5 using four approximating rectangles and right endpoints.R4= (b) Repeat part (a) using left endpoints.L4= (c) By looking at a sketch of the graph and the rectangles, determine for each estimate whether is overestimates, underes- timates, or is the exact area.?1.R4 ?2.L4
Correct Answers:
3*(1/2+1/3+1/4+1/5)
3*(1+1/2+1/3+1/4)
U O 2.(1 point) (a) Estimate the area under the graph off(x) =1+x 2 from x=1 tox=2 using three approximating rectangles and right endpoints.R3= (b) Repeat part (a) using six approximating rectangles and right endpoints.R6= (c) Repeat part (a) using three approximating rectangles and left endpoints.L3= (d) Repeat part (a) using six approximating rectangles and left endpoints.L6= (e) Repeat part (a) using three approximating rectangles and midpoints.M3= (f) Repeat part (a) using six approximating rectangles and midpoints.M6= Based on sketches of the graph off(x)and the approximat- ing rectangles, which appears to be the best estimate?A.M3 B.L3 C.L6 D.R3 E.M6 F.R6
Correct Answers:
3*1+5
0.5*(6*1+31/4)
3*1+2
0.5*(6*1+19/4)
3*1+11/4
0.5*(6*1+47/8)
E 3.(1 point) The speed of a runner increased during the rst three seconds of a race. Her speed at half-second intervals is given in the table.Find the best possible lower and upper estimates for the distance that she traveled during these three seconds. The answer to this problem requires that you enter the correctunits.t(s) 00:51:01:52:02:53:0 v(ft=s)05:510:615:117:119:520:4 Lower estimate = Upper estimate =
Correct Answers:
33.9 ft 44.1 ft 4.(1 point) A table of values of an increasing functionfis shown. Use the table to nd lower and upper estimates for R 25
f(x)dx:
x 0 5 10152025 f(x)42372561536 Lower estimate = Upper estimate =
Correct Answers:
-475 -85 5.(1 point) The velocity graph of a car accelerating from rest to a speed of 120 km/h over a period of 30 seconds is shown. Use the Mid- point Rule withn=6 to estimate the distance (in km) traveled during this period.Distance traveledkm
Correct Answers:
1/720*(31.25+66+88+103.5+113.75+119.25)
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