Which of the following represents the are a of the surface of the portion of the cylinderx² + z?= 4 that is inside the cylinder x +y = 4?V4-x²116 fo Sody dx4-x216 f S4-x21dx dyVA-4-x216 SoV4 - x² dx dy4-x216 V4 - x² dy dx

We need to find the integral which represents the area of the given surface. This can be done as…

Answered: Which of the following represents the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Determine which of the following gives the area of the surface obtained by revolving the curve y = 1/x, 1
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…
The area of the surface obtained by rotating the curve e asxsb, about the x-axis is 9. X 1/2 e2 + e 2 dx e2 + e 2 dx 2 e + e 2 dx e2 + e 2 dx 9. e2 + e 2 dx

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Which of the following represents the are a of the surface of the portion of the cylinde 2+ z? = 4 that is inside the cylinder x + y = 4? 1 16 o S dy dx 4-x² 16 4-x2 S dx dy 4-x2 16 S V4 - x² dx dy 16 4-x² dy dx