(1 point) The figure below shows contours of g(r, y) on the region R, with 9<...
and the r-axis. 5. Consider the region S bounded by r 1, r = 5, y (a) Use four rectangles and a Riemann sum to approximate the area of the region S. Sketch the region S and the rectangles and indicate your rectangles overestimate or underestimate the area of S. (b) Find an expression for the area of the region S as a limit. Do not evaluate the limit.
and the r-axis. 5. Consider the region S bounded by r...
9. (10 points) Evaluate S SR(2x2 - xy - y2)dA, where R is the region bounded by y = -2x +4, y = -2x + 7, y = x - 2, and y = 1 +1.
(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /0.25ry. (a) Find reasonable upper and lower bounds for JR f dA without subdividing R. upper bound lower bound (b) Estimate JRf dA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates overestimate: Inf dA underestimate: JRfdA average:...
2. (Objl) Consider the shaded region shown below 2 9(3) 6 2 (a) Find an overestimate of the area using 4 rectangles. (b) Find an underestimate of the area using 4 rectangles
2. (Objl) Consider the shaded region shown below 2 9(3) 6 2 (a) Find an overestimate of the area using 4 rectangles. (b) Find an underestimate of the area using 4 rectangles
The figure to the right shows Jill's budget constraint and her utility maximizing bundle (point R). What happens to her optimum if her income increases by 25%? 1.) Use the line drawing tool to show the new budget line. Label this line 'L 2.. 2.) Use the point drawing tool to locate a new consumer optimum if good Y is an inferior good. Label this point 'T'. 25- 24- 23- 22- 21- 20- 19- 18- 17- 16- 15- 14- 13-...
The figure shows the equipotential contours in the plane of two point charges. The labels on the contours are in V. Determine for each of the following statement whether it is true or false -10 1.8 2.7 6.0 6.0 2.2 1.8 10 1.4 20 20 10 20 x axis (m) TrueThere is a point along the line y 0 and between x-10 and +10 where the field is zero FalseThe above charge configuration can be described as an electric dipole....
6. (4 pts) Consider the
double
integral∫R(x2+y)dA=∫10∫y−y(x2+y)dxdy+∫√21∫√2−y2−√2−y2(x2+y)dxdy.(a)
Sketch the region of integration R in Figure 3.(b) By completing
the limits and integrand, set up (without evaluating) the integral
in polar coordinates.∫R(x2+y)dA=∫∫drdθ.7. (5 pts) By completing the
limits and integrand, set up (without evaluating) an iterated
inte-gral which represents the volume of the ice cream cone bounded
by the cone z=√x2+y2andthe hemisphere z=√8−x2−y2using(a) Cartesian
coordinates.volume =∫∫∫dz dxdy.(b) polar coordinates.volume
=∫∫drdθ.
-1 -2 FIGURE 3. Figure for Problem 6. 6. (4 pts)...
22 (1 point) a) The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) on the interval (2,6]. 9 The value of this Riemann sum is and this Riemann sum is an underestimate of the area of the region enclosed by y = f(x), the x-axis, and the vertical lines x = 2 and x = 6. y 8 7 6 5 4 3 2 1 X 1 2 3 4 5 6 7 8 Left...
pl pl-y The figure below shows the region of integration for the integral [ f(, y, z) dz dy dx. Jo Jo Jo Rewrite this integral as an equivalent iterated integral in the five other orders. z=1-y y=vx 0 1 y
The figure below shows a curve C, parametrized by (a) The point P lies on C, and its r-coordinate is 4. Find the value of t at the point P according to the parametrization, and find the y-coordinate of P. equation in terms of r and y. line 4. as shown shaded in the figure. Find the area of R. (b) The line is normal to C at the point P. Express the line l using an (c) The bounded...