1. Let R be the region enclosed between the circles r² + y? = 81 and r² + y? = 100. To measure the area of R correct formulation is /2 (100 A=0 Jr=9 -10 C. Se-o 930 Jr=3 /2 10 r dr de D. S, r dr de r2m r10 e=0 Jr=3 2. Domain of function f(r, y) = e+v +1 В. R? C. {(r, y) : r, y 0} А. R D. попe

Calculus: Early Transcendentals
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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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1. Let R be the region enclosed between the circles r? + y? = 81 and r? + y? = 100. To measure the area
of R correct formulation is
A. /2 r100
B. ES, r dr dð
C. Se-o
D. S, r dr de
Jag rdr de
e=0
10
930 Jr=3
/2 10
Jrs9
r2m
Je30 Jrm3
r dr de
10
2. Domain of function f(r, y) = e*+y +1
A. R B. R C. {(r, y) : 1, y 20} D. none
3. In which region on ry-plane the function f(x,y)=ln(x+y) is not continuous?
A. except r = 0 B. except y = 0 C. except r = 0 and y = 0 D. none
4. Assume that f (1,2) = 4 and f (x, y) is differentiable at (1,2) with fx (1,2) = 2 and fy (1,2) = 3. Estimate
the value of f (0.9,1.950).
А. 3.65 В. 3 С. 4,21
D. 5
5. If the gradient of f(x, y) at (1,2) is 2i – 2j, then the maximum and minimum values for a directional
derivative of f at (1, 2) are respectively
A. 2/2 and -v2 B. -2/2 and v2 C. 2/2 and 2v2 D. 2/2 and -2/2
6. Suppose the second-order partial derivatives of the function f(r, y) exists at thr critical point (0,0).
Which of the following one is true for the critical point to be maximum?
A. frz (0,0) = 2 fyy(0,0) = 2 and zy(0,0) = 4
C. fz (0, 0) = 4 fyy (0, 0) = 4 and rry(0,0) = 4 D. faz (0,0) = -4 fyy (0,0) = -4 and rry (0,0) = 4
B. fzz (0,0) = 2 fyy (0, 0) = 2 and rzy (0,0) = 2
7. A line initiated from (1,0,2) and parallel to a vector i+j+k what is the parametric equation of the line
(if t is a parameter)?
A. x=1+ 2i, y= 2j , z= 2+j B. x=1+ 2t, y= 2t C. x=1+ t, y= t , z= 2+t D. x=2+ i, y= 1,
z= 2+t
8. || dA measure
R
A. volume of R
B. height of the surface C. area of R D. all of these
9. Find S-o dA, where r is a radius of a circle
А. 2т
=0 Jr=0
В. п/2 С. 4т D. п/4
10. Which of the following is not a function of f : R2² → R?
A. f(r, y) = e" B. f(r, y) = 1 C. f(r, y) = ey +1 D. f(x) = e"
Transcribed Image Text:1. Let R be the region enclosed between the circles r? + y? = 81 and r? + y? = 100. To measure the area of R correct formulation is A. /2 r100 B. ES, r dr dð C. Se-o D. S, r dr de Jag rdr de e=0 10 930 Jr=3 /2 10 Jrs9 r2m Je30 Jrm3 r dr de 10 2. Domain of function f(r, y) = e*+y +1 A. R B. R C. {(r, y) : 1, y 20} D. none 3. In which region on ry-plane the function f(x,y)=ln(x+y) is not continuous? A. except r = 0 B. except y = 0 C. except r = 0 and y = 0 D. none 4. Assume that f (1,2) = 4 and f (x, y) is differentiable at (1,2) with fx (1,2) = 2 and fy (1,2) = 3. Estimate the value of f (0.9,1.950). А. 3.65 В. 3 С. 4,21 D. 5 5. If the gradient of f(x, y) at (1,2) is 2i – 2j, then the maximum and minimum values for a directional derivative of f at (1, 2) are respectively A. 2/2 and -v2 B. -2/2 and v2 C. 2/2 and 2v2 D. 2/2 and -2/2 6. Suppose the second-order partial derivatives of the function f(r, y) exists at thr critical point (0,0). Which of the following one is true for the critical point to be maximum? A. frz (0,0) = 2 fyy(0,0) = 2 and zy(0,0) = 4 C. fz (0, 0) = 4 fyy (0, 0) = 4 and rry(0,0) = 4 D. faz (0,0) = -4 fyy (0,0) = -4 and rry (0,0) = 4 B. fzz (0,0) = 2 fyy (0, 0) = 2 and rzy (0,0) = 2 7. A line initiated from (1,0,2) and parallel to a vector i+j+k what is the parametric equation of the line (if t is a parameter)? A. x=1+ 2i, y= 2j , z= 2+j B. x=1+ 2t, y= 2t C. x=1+ t, y= t , z= 2+t D. x=2+ i, y= 1, z= 2+t 8. || dA measure R A. volume of R B. height of the surface C. area of R D. all of these 9. Find S-o dA, where r is a radius of a circle А. 2т =0 Jr=0 В. п/2 С. 4т D. п/4 10. Which of the following is not a function of f : R2² → R? A. f(r, y) = e" B. f(r, y) = 1 C. f(r, y) = ey +1 D. f(x) = e"
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