Calculate Sle30?tºgº da dy, where D is the interior of the ellipse (x) + (*) <1....
Evaluate // e-(x+vº)dA where D = {(x,y): x2 + y2 <1,1 20, y 2 0}.
Find the length s of the path (2 + 141, 3 +212) over the interval 7 <1 38. (Express numbers in exact form. Use symbolic notation and fractions where needed.) s= Find the length s of the path (r + 5,12 + 8) over the interval 5 <1 37. (Use symbolic notation and fractions where needed.) S =
Use spherical coordinates to calculate the triple integral of f(x, y, z) = y over the region x2 + y2 + z2 < 3, x, y, z < 0. (Use symbolic notation and fractions where needed.) S S lw y DV = help (fractions)
Exercise 4.9.15. Find a continuous function defined in the region (x/2)+(/3)< 1 (i.e., the interior of an ellipse) that has neither a marimum nor a minimum but is bounded.
Integrate Sc(x) di where C is the graph of y =lnx for 152<2.
The demand for a product is given by D(x) = 200e -0.025x, where x is the number of units sold each week and 0 < x < 70. Step 1 of 2: Find the number of units sold that will yield maximum revenue. Round your answer to the nearest whole unit. Keypad Answer How to enter your answer units
3. Draw the region D and evaluate the double integral using polar coordinates. dA, D= {(x, y)| x2 + y² <1, x +y > 1} (b) sin(x2 + y2)dA, D is in the third quadrant enclosed by D r? + y2 = 7, x² + y2 = 24, y = 1, y = V3r.
Let X N(1,3) and Y~ N(2,4), where X and Y are independent 1. P(X <4)-? P(Y < 1) =? 4、 5, P(Y < 6) =? 7, P(X + Y < 4) =?
dV, where is the unit ball in R3, that is, Use spherical coordinates to compute the integral We E = {(x, y, z)| 22 + y2 + 2 <1}.
Let X be a banach space such that X= C([a,b]) where - ab+ with the sup
norm. Let x and f X. Show
that the non linear integral equation
u(x) = (sin
u(y) dy + f(x) ) has a solution u X. (the integral is
from a to b).
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