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Question 5 Choose the correct integration that gives the volume of the solid under 2 =...
concisely working please the correct answer is A
2x is the base of a solid. For the solid, each cross section andy 23. The region enclosed by the graphs of y dicular to the y-axis is a rectangle whose height is 3 times its base in the xy-plane. Which of the llowing expressions gives the volume of the solid? Jo 3 (2x x) dx 3「(2x+x2)2 dr + x (D)
2x is the base of a solid. For the solid, each...
10. Find the volume of the solid under the plane x – 2y + z = 5 and above the region bounded by y = 1- x and y = 1-x2. Sketch the region of integration first!
7. Find the volume of the solid region that lies under the surface 2 = ry and over the region in the xy plane bounded by the curves y = 2r and y = r A. 4/3 B. 8 C. 8/3 D. 32/3 E. none of the above 8. Evaluate SSSE Vx2 + y2 dV where E is the region bounded by the paraboloid z = x2 + y2 and the plane z = 4. A. 87 B. 327 c....
Find the volume of the solid obtained by rotating the area under the graph of y=x2(1-x2)1/2 over the interval (0,1) about the y axis.
(a) Evaluate the double integral 4. (sin cos y) dy dr. Hint: You may need the formula for integration by parts (b) Show that 4r+6ry>0 for all (r,y) ER-(x,y): 1S2,-2Sysi) Use a double integral to compute the volume of the solid that lies under the graph of the function 4+6ry and above the rectangle R in the ry-plane. e) Consider the integral tan(r) log a dyd. (i) Make a neat, labelled sketch of the region R in the ry-plane over...
Goal: Use integration to derive the volume of the solid sphere in dimensions above 3 (R4, Rʻ,...). Notation & Terminology: Use V, and S, for the "volume" and "surface area" of an n- dimensional solid sphere. Thus "Volume" is not always in cubic units, it is in units^n. So, similarly “surface area" is in units (n-1) and is the measurement of the boundary. 1. Look up & become familiar with the formulas for V, and S. Start in R', what...
Question 8 Find the volume of the solid obtained when the region bounded by the line y - 2x, the line x = 3, and the x-axis is rotated about the y-axis. Not yet answered Select one: Marked out of 1.00 3.48 b. 30 P Flag question C. 36 d. 16 Question Let f(x) = Si (31²+1 - dt. Find f'(1). 14+2 Not yet answered Select one: Marked out of 1.00 a. 1/3 P Flag question b. 4/3 o c....
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question Evaluate the integral. 5 In 5 1) S. ey dx dy el B) 4 A) 8 D) 9 C) 18 Integrate the function f over the given region. 2) f(x, y)- over the trapezoidal region bounded by the x-axis, y-axis, line x -5, and line 9 D) 60 A) 25 B) 40 C) 30 Write an equivalent double integral with the order of integration reversed....
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
CALCULUS Consider the function f : R2 → R, defined by ï. Exam 2018 (a) Find the first-order Taylor approximation at the point Xo-(1, -2) and use it to find an approximate value for f(1.1, -2.1 (b) Calculate the Hessian ã (x-xo)' (H/(%)) (x-xo) at xo (1,-2) (c) Find the second-order Taylor approximation at Xo (1,-2) and use it to find an approximate value for f(1.1, -2.1) Use the calculator to compute the exact value of the function f(1.1,-2.1) 2....