1. The figure shows level curves of a function in the region R=0,6 x 0,6]. Use...
RogaCalcET3 14.5.003. My Notes 1 -/1 points The figure below shows the level curves of a function fx, y) and a path r ), traversed in the direction indicated. State whether the derivative frt is positive, negative, or zero at points A-D. 8 4 -10 B. 0 A 20. 30 -4 At point A the derivative is -Select At point B the derivative is-Select At point C the derivative is-Select At point D the derivative is --Select Show My Work...
Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves. Then find (approximately- three decimal places) the area of the region bounded by the curves. Also, make a rough sketch of the region sought. You must write the definite integral using proper notation to receive full credit 1) y = χ sin(x*) , y = x6
Directions: Use the graph to find approximate x-coordinates of the points of intersection of the given curves....
(1 point) The figure below shows contours of g(r, y) on the region R, with 9< < 15 and 4< y < 10 10 7 6 4 6 11 13 15 SR 9(z, y) dA Ay 2, find an overestimate and an underestimate for Using Ar Overestimate Underestimate =
(1 point) The figure below shows contours of g(r, y) on the region R, with 9
e ana the gradient IV.1 The level curves of the function z fix, y) are sketched in the figure below: 20 50 100 10 150 10 20 30 Let u= (l,-) and v=죠(1,1) Estimate the derivatives at the indicated point: DJい IV.2 (The Directional Derivative) Compute the derivative of the function f(x,y,z)-sin(2x-y)+ cos(2y-2) Ft%r,-r) in the direction of the vector". (-2,-1, 2) at the point
e ana the gradient IV.1 The level curves of the function z fix, y) are...
Suppose R is the shaded region in the figure, and f(x,y) is a continuous function on R. Find the limits of integration for the following iterated integrals. BD (a) [f $12,9)da = S, "Lº f12, y) dy de PH dA= JE JG f(x,y) dc dy I
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Problem #4: Which of the following are level curves for the function f(x,y)-ino-e-r ) ? 1
Problem #4: Which of the following are level curves for the function f(x,y)-ino-e-r ) ? 1
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6. (3 pts.) Let R be the region colored in black in the figure below. The two curves bounding R are the circle 12 + y2-= 1 and the curve described in polar coordinates by the equation r-2 sin(20). Set up but do NOT evaluate a (sum of) double integral(s) in polar coordinates to find the area of R. We were unable to transcribe this image
6. (3 pts.) Let R be the region colored...
5) The level curves of a function f(x,y) are given in the graph below. 2 X -1 -2 i Estimate f(3,3) ii Estimate Vf(-3, 1) Let u be a unit vector parallel to (1,4). Calculate Daf using your answer from i iv) Find the location of all critical points of the function f, on the set -5 <r< of these is a saddle point) iii) Let D be the domain bounded between the curves y = x and y= 2...
2. (2 points) Use the midpoint rule to estimate (7 – 2x – y)dA over the region D = {(x,y): -1 <r<2, -15y<2} partitioned using the lines x = 0, x = 1 and y = 0, y = 1. Take the sample points to be the midpoints of the sub-rectangles.
- -- - --10--- The region R is bounded by the curves y = 3.x, y = 9 - 22, and the y-axis, and its density is 8(x, y) = sy. To find the center of gravity of the pd (3) pdf92) pd 9() region you would compute 8(2,y)dA=1 62, y)dydx, 28(2,y)dydx, and 1 y(x,y)dyd. where Jc Jp(x) Je Jp(2) Jp(2) c= d= p(2) = 9(x) = pa pa(z) I dyda = Jo Ipa) 1 xdydx = I ydydx =...