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5.7 Exercises sing only the definition of the integral, show that (assuming the inte grals exist)...
ense only if the integrand, (x),is a useful to extend to definition of the inte hen y-fa) has a vertical asymptote in we are integrating extends to positive o dx,for which the interval of integra ed sinceapprowches +u a is surely a famillar techeique by now omipute ?? k to all the other times this approach has s areas of plane ngions, finding volumes of otherwise difficult quantity Here is an example that exhibits delete shift alr mmand option
1 4. For each of the following, compute the integral or show it doesn't exist: (a) Sr3 1+z2+y2 +220V (b) Sc 1027y2y2dA where C {(x, y) : x2 + y2 <1} (C) Ss zvydA where S = = {(x,y) : 1 < x, 0 }
4. For each of the following, compute the integral or show it doesn't exist: 2 1 (a) SR3 dV R3 1+x2 + y2 +22 (b) Sc (22+42 2dA where C = {(x,y) : x2 + y2 < 1} (c) Ss zvydA where S dA where S = {(x, y):1 < x,0 <y <} 1 9 9
Question 2 please 1 and 2, determine whether or not the integral is In exercises improper. If it is improper, explain why 12. (a) 12 x-2/5 dx 「x-2/5 dx 「x2/5 dx (b) (c) I. (a) 0 13. (a 40 1 dx 2 x 14. (a In exercises 3-18, determine whether the integral converges or diverges. Find the value of the integral if it converges. 15. (a (b)人1x-4/3 dr 3, (a) l.lyMdx (b) x43 dx 16. (a 4. (a) 45 dx...
1. Use the definition of integral to show that if f : B → R and f are integrable, then Inf e f 2. Find the volume of the region K between ~ = x2 + 9y2 and z = 18-x2-9y2 (Use Fubini's Theorem) 3. Evaluate Jryz where S is the upper half of the unit sphere. (Use Change of Variable Theorem)
please show all work and steps thank you :) Evaluate the integral. 1 $5x(x2 - 1) '?dx 0 1 5x(x2 - 1)?dx = (Type an integer or a simplified fraction.) 0
only the ones highlighted and please show all steps. Finding Area by the Limit Definition In Exercises 47–56, use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region. 47. y = - 4x + 5, [0, 1] 48. y = 3x - 2. [2,5] 49. y = x2 + 2, [0, 1] 50. y = 5x + 1, [0, 2] 51. y...
Only #2 please show work! Exercises In Exercises 1-4,1 surface, oriented with an upward-pointing normal same ses 1-4, verify Stokes' Theorem for the given vector field and 8.1 (2ХУ, Х, У + z), the surface z 1-x2-y2 for betw norn 9. bet nor r+y h2. F (yz, 0,.x), the portion of the plane1 where r, y,z0
3. a) Let f(x) = 2x3 – 4.. Use only the definition of derivative to compute f'(1). b) Using only the definition of right derivative, show that if f(x) = x1/4 then f4 (0) does not exist.
Find the limit and show steps if doesn't exist please I'll rate: (a) lim -3.x2 + 8 X400 5x2 + 12x (b) lim 3 + 7:22 2x – 9 0-00 Use the limit definition of the derivative to find f'(x) if f(x) = x2 + 50.