solution and answer guide for Calculus: Concepts and Contexts, 5th Edition by James Stewart and Kokoska

SolutioncandcAnswercGuide:cStewartcKokoska,cCalculus:cConceptscandcContexts,c5e,c2024,c9780357632499,cChapterc2:cSectioncConceptcCheck



SOLUTION AND ANSWER GUIDE c c c



CALCULUS 5TH EDITION JAMES STEWART, KOKOSKA
C C C C C



Chapterc1-13



CHAPTER 1: SECTION 1.1 TAB
C C C C




LE OF CONTENTS
C C




EndcofcSectioncExercisecSolutions ............................................................................................................... 1




END OF SECTION EXERCISE SOLUTIONS
C C C C




1.1.1
(a) cfc(1)cc3
(b) fc(1)cc0.2
(c) fc(x)cc1c whencxc=c0candcxc=c3.
(d) fc(x)cc0cwhencxc≈c–0.8.
(e) Thecdomaincofcfcisc2ccxcc4.cThecrangecofcfcisc1cc ycc3.
(f) fc iscincreasingconcthecinterval2ccxcc1.

1.1.2
(a) fc(4)cc2;c g(3)cc4
(b) fc(x)cc g(x)cwhencxc =c–2c andc xc =c2.

(c) fc(x)cc1cwhencxc≈c–3.4.

(d) fciscdecreasingconcthecintervalc 0ccxcc4.

(e) Thecdomaincofcfcisc4ccxcc4.cThecrangecofcfcisc2ccycc3.

(f) Thecdomaincofcgcisc4ccxcc4.cThecrangecofcgcisc0.5ccycc4.



1.1.3



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(a) fc(2)cc12 (b) fc(2)cc16 (c) fc(a)cc3a2ccacc2
(d) fc(a)cc3a2ccacc2 (e) fc(ac1)cc3a2cc5acc4 (f) 2cfc(x)cc6a2cc2acc4
(g) fc(2a)cc12a2cc2acc2 (h) fc(a2)cc3a4cca2cc2


(i) cfc(a) c 3a2ccacc2 
2c 2c
c9a4cc6a3c13a2cc4acc4
(j) fc (acch)cc3  a cch cacchcc2cc3a2c c3h2c c6ahccacchcc2
2c




1.1.4

fc(3cch)ccfc(3)c (4cc3(3cch)cc(3cch)2c)cc4c 9cc3hcc9cc6hcch2)c 3hcch2c
c c c c (3 h)
h h h h


1.1.5 

a3cc3a2hcc3ah2cch3cca3  hc3a cc3ahcch  3a2  3ah  h2
2 2
fc(acch)cc fc(a)c
 c c c c c

h h h


1.1.6

1c 1 ac x
c c 1
fc(x)cc fc(a)c axc  accx cc

   





 x a c
c ax  




xcca xcca xcca ax(xcca) ax



1.1.7

xcc3c 1c3 xcc3c xcc3cc2xcc2 xc1c xc1
c c2
fc(x)ccfc(1)c xc1 11 c  xc1
  xc1 
xc1c
cc xc1c c 1
xc1 xc1 xc1 xc1 xc1 xc1 xc1


1.1.8

xcc4c
Thecdomaincof fc(x)c isc xc |cxcc3,3.
x2cc9

1.1.9 
 
2x3cc5
Thecdomaincof fc (x)c 2 iscxc |cxcc3,c2.
x ccxcc6



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1.1.10 

Thecdomaincof fc(t)c 3c2tc1 iscallcrealcnumbers.


1.1.11 

gctcc  iscdefinedcwhenc3cctcc0cctcc3candc 2cctcc0cctcc2.cThus,cthecdomaincisc tcc2,
orc ,c2.

1.1.12

1
Thecdomaincofc h(x)c c isc,c0c5,c.


1.1.13

Thecdomaincofc F( cp)c 2c p is0cc pcc4.

1.1.14
uc1
Thecdomaincofc fc(u)c iscuc |cucc2,c1.
1
1
uc1
1.1.15
(a) Thiscfunctioncshiftscthecgraphcofcyc=c|x|cdownctwocunitscandctocthecleftconecunit.
(b) Thiscfunctioncshiftscthecgraphcofcyc=c|x|cdownctwocunits
(c) Thisc functioncreflectscthecgraphcofcyc=c|x|caboutcthecx-
axis,cshiftscitcupc3cunitscandcthenctocthecleftc2cunits.
(d) Thiscfunctioncreflectscthecgraphcofcyc=c|x|caboutcthecx-axiscandcthencshiftscitcupc4cunits.
(e) Thisc functioncreflectscthecgraphcofcyc=c|x|caboutcthecx-
axis,cshiftscitcupc2cunitscthencfourcunitsctocthecleft.
(f) Thiscfunctionciscacparabolacthatcopenscupcwithcvertexcatc(0,c5).cItciscnotcactransformationcofc yc=c|x|.


1.1.16

(a) gccfc x   ccgc x 2 c1c 10  x 2 c1

(b) fcgc4ccfc104cc402c1cc1601

(c) gc g c1cc gc101cc1010cc100



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(d) 
fc g ccfc2    
c cfc g c 2 c1
2
 f 105 f 50  502 1  2501
c c c c c c c c c c c




(e) 1 1 1 1

    
fc g ccx fc 10x 10x
2c
1 100x2c c1

1.1.17

Thecdomaincofc h(x)c 4ccx2 isc2ccxcc2,candcthecrangecis
0  y  2. The graph is the top half of a circle of radius 2 with center at the o
c c c c c c c c c c c c c c c c c c c c c


rigin.


1.1.18
Thecdomaincof fc(x)cc1.6xcc2.4c iscallcrealcnumbers.




1.1.19 
 
t 2 c1
Thecdomaincof g(t)c  istc |ctc c1.
tc1




1.1.20 

xc1 
fc (x)c
Thecdomaincof x 1c isxc |cxcc1,1.
2c




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