4.Find the mass and center of mass of a wire in the shape of the helix x = t, y = cost, z = sint, 0≤t≤ 2πif the density at any point is equal to the square of the distance from the origin. (Hint: square of distance is(x² + y² + z²))

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Answered: 4. Find the mass and center of mass of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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16:24 O * l 87%i Home wroke2.pdf (ans. : a )Vx,0 0; c)x 0) 16. Find the points of intersection of .x' = 4y and y= 4x. (ans.:(0,0,(16,64) 17. Find the coordinates of the points at which the curves cut the axes : a) y=x' -9x' , b) y=(x'-1)(x* - 9) , c) y=(x+1\(x-5} (ans.a)(0,0;(,0,9,0;b)(0,9;(1,0,(-1,),(3,0),(-3,0;c/(0,25;(-10),50) poo0000000oooo000000ooo000000g 20. If flx) = 1/x and g(x}=1/^x ,what are the domain of f, g , ftg , f-g, fg, f'g, g/f, fg and gf ? What is the domain of h(x) =g(x+4) ? (ans.: Vx + 0,Vx> 0,Vxr>0,Vx>0,Vx>0,Vx>0,Vx2 0,Vx 2 0,Vx> 0;Vx>4) 21. Discuss the continuity of : x+- for x 2 (ans.: discontinuous at x=0,2 ; continuous at x=1) 22. Evaluate the following limits : x+ Sinx 1+ Sinx a) lim -* 2x + 5 b) lim x. Sinx c) lim 1-+* tan 3x d) lim N (x+ Sinx ) Vx +1- 2x f) lim 1- Vx e) lim 1-X g) lim(Vn' +1 -n) x' -x (ans.:a)1/2, b)0, c)1/3, d)0, e)1/2, )-1/22, g)0) f(x) for x+ 3 23. Suppose that : flx) = x² – 3x² -4x +12 and h(x)={x- 3 k for x= 3) Find : a) all zeros of…

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4. Find the mass and center of mass of a wire in the shape of the helix x = t, y = cost, z = sint, 0≤t≤ 2π if the density at any point is equal to the square of the distance from the origin. (Hint: square of distance is (x² + y² + z²))