n Exercises 1-12, evaluate the indicated limit or explain why itdoes not exist.sin(xy)2x2 - ху9.lim10.lim(r,y)-(0,0) x2 + y2(x.y)(1,2) 4x2-y21.limxy +x22.Vx2 + y2lim(x.y) (2,-1)11.lim(r,y)(0,0) x2 + v413. Kow can the functionT(x.y) (0,0)lim(r,y)(0,0) 2r4+ y4x² + y?3.lim4.limx2 +y2-x'y3(x.y) (0,0)y(x.y) (0,0) x2 + y?f(x.y)%D(x. y) # (0.0).x2 + y2cos(xy)x(y-1)2be defined at the origin so that it becomes continuous at allpoints of the xy-plane?5.lim6.X.y)(I.) 1-XIcos ylim(x.y) (0.1) x2 +(y-1)214. How can the function7.sin(x - y)x-ylim(r.y) (0,0) X2+ y28.lim(x.y)-(0,0) Cos(x + y)f(x, y) =(x#y).x-y

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x2y2 lim (r,y)(0,0) 2r+ y

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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In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Question

n Exercises 1-12, evaluate the indicated limit or explain why it
does not exist.
sin(xy)
2x2 - ху
9.
lim
10.
lim
(r,y)-(0,0) x2 + y2
(x.y)(1,2) 4x2-y2
1.
lim
xy +x2
2.
Vx2 + y2
lim
(x.y) (2,-1)
11.
lim
(r,y)(0,0) x2 + v4
13. Kow can the functionT
(x.y) (0,0)
lim
(r,y)(0,0) 2r4+ y4
x² + y?
3.
lim
4.
lim
x2 +y2-x'y3
(x.y) (0,0)
y
(x.y) (0,0) x2 + y?
f(x.y)%D
(x. y) # (0.0).
x2 + y2
cos(xy)
x(y-1)2
be defined at the origin so that it becomes continuous at all
points of the xy-plane?
5.
lim
6.
X.y)(I.) 1-XIcos y
lim
(x.y) (0.1) x2 +(y-1)2
14. How can the function
7.
sin(x - y)
x-y
lim
(r.y) (0,0) X2+ y2
8.
lim
(x.y)-(0,0) Cos(x + y)
f(x, y) =
(x#y).
x-y

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