OC userin Calculus·22 Oct 2019Let a solid R of constant density δ(x, y, z) = 1 occupy the portion of the sphere x2 + y2 + z2 < 4 which is in the first octant. Use spherical coordinates to compute the moment of inertia with respect to the z axis. 2 2
OC userin Calculus·29 Mar 2019 Q1 (4 points) Use Green's Theorem to find the counterclockwise circulation and outward flux for the vector field and curve C consisting of the segment of the parabola y z2 rom (0,0) to (1, 1), and the segment of the parabola z2 from (1, 1) to (0,0)
OC userin Calculus·13 Jul 2019 Use the following definition for area to answer Problems 2 and 3: Definition: The area A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approrimating rectangles: 2. Use the definition of area given above to find an expression for the area under the graph of f as a limit. Do not evaluate the limit 3. (a) Use the definition of area given above to find an expression for the area under the curve y from 0 to 1 as a limit. b) The following formula for the sum of the cubes of the first n integers is proved in Appendix F of your textbook. Use it to evaluate the limit in part (a) 13 + 23 +3°+ + n3 =[n(n + 1)
OC userin Calculus·12 Nov 2019 Apply Green's Theorem to evaluate the integral (32 - z)dz 2y)dy, where C is the triangle bounded by the lines y 0, z = 3 and y z with counterclockwise orientation.
OC userin Calculus·13 Nov 2019 (exercise 13.5, 8 points). ) Set up the iterated integral that computes the surface area of the given surface over the regiorn R. . (13.5-7). /(x,y) = sin x cos y; 2T. . (13.58). f(x,y) = ê³¼ê¸å¬R is the circle x2 + y2 = 9 .(13.5-9). f(x,y)=x2-y2; Ris the rectangle with opposite corners (-1,-1) and (1,1). R is the rectangle with bounds 0 Comments
OC userin Calculus·13 Feb 2019 Find the area of the shaded region. 23 23) 16,1 Graph the function fx) over the given interval. Partition the interval into 4 subintervals of equal length. Then add to your sketch the rectangles associated with the Riemann sum Σ ficklak using the indicated point in the kth subinterval for ck k-1 24) 24) f(x) - 2x 2. [0, 2], left-hand endpoint 05 i L.5 21
OC userin Calculus·17 Mar 2019 Consider the vector field Fy22)j yzk, defined on R3 1. Compute the curl of F 2. Use your answer to a) to explain why F cannot be a conservative vector field. 3 Verifty that div(curl F)-0
OC userin Calculus·30 Apr 2019 9.1.115 Question Help * The weights W1 and W2 exerted on each rafter for the roof truss shown in the figure to the right are determined by the system of linear equations.Solve the system. 150 pounds W 2W2 300 What is the weight applied to each rafter? w,-pounds (Round to the nearest tenth as needed.) W2-pounds (Round to the nearest tenth as needed.)
OC userin Calculus·25 May 2019How can I find the sum of part c)? Prove tha for all α with ë Comments
OC userin Calculus·18 Jan 2019 Compute the regression line for the points (-1, 1),(0-14) , and (1,7). Give the result as a function of x
OC userin Calculus·9 Oct 2019 Calculate the length of the curve C, defined by r()-(2 coso. 2 sinC) with domain of-Ï/2 t Comments
OC userin Calculus·16 Oct 2019Use upper sums to show that the area under the graph of y=x3 over the interval [0,b] is b4/4
OC userin Calculus·12 Jun 2019 Please I need help solving 7 and 8 Use the Fundamental Theorem of Line Integrals to evaluate [2xyzdr + x'zdy + x2 ydz where C is a smooth curve from (0,0,0) to (l,3,2) 7. 8. Evaluate Jxyd+ (r +y' )dy where C is the square with vertices (0, 0), (0, 1), (1, 0), and (1, 1) oriented counterclockwise.
OC userin Calculus·15 Oct 2019 4. Given f(x) = e"41, approximate the area under the graph of f(x) and above the x axis from x=0 to x = 2 using the following methods with n =4. NEATLY illustrate EACH on the graphs provided. Round final answers to 2 decimals. a) Use left endpoints b) Use right endpoints c) Use midpoints 3 of 3