Solution Manual For Calculus 5th Edition by James Stewart, Kokoska Chapter 1-13

Solutionand Answer Guide: StewartKokoska,Calculus:Conceptsand Contexts,5e,2024, 9780357632499,Chapter2:Section Concept Check
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SOLUTION AND ANSWER GUIDE ,l , l ,l




CALCULUS5THEDITIONJAMESSTEWART,KOKOSKA ,L ,L ,L ,L ,L




Chapter1-13 ,l




CHAPTER1:SECTION1.1 ,L ,L ,L




TABLE OF CONTENTS
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Endof SectionExercise Solutions................................................................................................................ 1
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ENDOF SECTIONEXERCISE SOLUTIONS,L ,L ,L ,L




1.1.1

(a) f(1)=3 ,l ,l ,l




(b) f(−1)−0.2 ,l ,l ,l




(c) f (x) =1 when x = 0 and x = 3. ,l ,l ,l , l ,l ,l ,l ,l ,l ,l ,l




(d) f(x)=0whenx≈–0.8. ,l ,l ,l ,l ,l ,l ,l




(e) Thedomainoffis −2x4.Therangeoffis −1 y3. ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l




(f) f isincreasingontheinterval−2 x1.
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1.1.2

(a) f(−4)=−2; g(3)=4 ,l ,l ,l , l ,l ,l




(b) f (x) = g(x)when x = –2 and x = 2. ,l ,l , l ,l ,l , l ,l ,l ,l , l ,l




(c) f(x)=−1 whenx≈ –3.4. ,l ,l ,l ,l ,l ,l ,l




(d) fisdecreasingontheinterval 0x4.
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(e) Thedomainoffis −4 x4.Therangeoffis −2 y3. ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l




(f) Thedomainofgis −4x4.Therangeofgis 0.5 y4. ,l ,l ,l ,l , l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l




1.1.3



©2024Cengage. AllRightsReserved. Maynotbescanned,copied orduplicated,orposted toapubliclyaccessible
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1
website,inwholeorin part. ,l ,l ,l ,l ,l

,Solutionand Answer Guide: StewartKokoska,Calculus:Conceptsand Contexts,5e,2024, 9780357632499,Chapter2:Section Concept Check
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(a) f(2)=12 ,l ,l ,l



(b) f(2)=16 ,l ,l ,l



(c) f (a) =3a2 −a+2
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(d) f (−a)=3a2 +a+2
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(e) f(a+1)=3a2 +5a+4 ,l ,l ,l ,l ,l ,l ,l ,l (f) 2f (x)=6a2 −2a+4 ,l ,l ,l ,l ,l ,l ,l ,l




(g) f (2a) =12a2 −2a+2
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(h) f (a2) =3a4 −a2 +2
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(i) f(a) = 3a2−a+2 ( )
2 2
=9a4−6a3+13a2−4a+4
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(j) f (a+h) =3 ( a +h) −(a+h)+2 =3a2 +3h2 +6ah−a−h+2
2 , l




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1.1.4

f(3+h)−f(3) (4+3(3+h)−(3+h)2)−4 9+3h−9−6h−h2) −3h−h2
= = = =− (3 + h)
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,l ,l ,l ,l




h h h h


1.1.5

f(a+h)− f(a) a3+3a2h+3ah2+h3−a3 h ( 3a2+3ah+h2 ) =3a2+3ah+h2
=
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=
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,l ,l ,l ,l ,l




h h h


1.1.6

1 1 a x
− −
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f(x)− f(a) 1
a−x =−
  
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= x a = ax ax , l



, l
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,



= l







x −a ,l ,l x −a x −a ax(x−a) ax ,l ,l ,l ,l ,l ,l




1.1.7

x+3 1+3 x +3 x+3−2x−2 −x +1 x−1
− −2
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f(x)− f(1) x+1 1+1 = x+1 x+1 x + 1 = − x +1 = − 1
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= = =
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x−1 ,l
x−1 x−1 ,l ,l
x−1 x −1 x−1 x+1 ,l ,l ,l ,l
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1.1.8
x +4
is x |x  −3,3.
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Thedomain of f(x)= , l ,l




x −9
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2
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1.1.9

2x3 −5
f (x) = isx |x−3,2.
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Thedomain of
x2 +x−6
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©2024Cengage. AllRightsReserved. Maynotbescanned,copied orduplicated,orposted toapubliclyaccessible
,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l

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,Solutionand Answer Guide: StewartKokoska,Calculus:Conceptsand Contexts,5e,2024, 9780357632499,Chapter2:Section Concept Check
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1.1.10

Thedomain of ,l ,l
f(t)= ,l ,l
3
2t−1 isall realnumbers.
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1.1.11

g(t)=
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− isdefinedwhen3−t0t3and 2−t0t2.Thus,thedomainis t2,
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or (−,2.
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1.1.12

1
The domain of h(x) = − ,l ,l , l ,l , l is (−,0)(5,).,l ,l
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1.1.13

The domain of F( p)= ,l ,l , l ,l ,l 2− ,l p is0 p4. ,l , l ,l ,l




1.1.14
u+1
The domain of f (u)= isu |u  −2,−1.
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1
1+
u+1 ,l




1.1.15
(a) Thisfunction shifts thegraph of y= |x|down two units andtotheleft one unit.
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(b) Thisfunction shiftsthegraph of y= |x|down two units ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l




(c) This function reflects the graph of y = |x|about the x-axis, shifts it up 3units and then totheleft2 units.
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(d) Thisfunction reflectsthe graph of y= |x|about thex-axis andthen shifts it up4 units.
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(e) This function reflects the graph of y = |x|about the x-axis, shifts it up 2unitsthen four units tothe left.
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(f) Thisfunctionis aparabolathat opens upwith vertex at(0,5). It is not atransformation of y= |x|.
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1.1.16

(a) g(f( x ) ) =g( x 2 +1)=10 ( x 2 +1)
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(b) f(g(4))= f(10(4))=402+1=1601
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(c) g( g (−1))= g(10(−1))=10(−10)= −100
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©2024Cengage. AllRightsReserved. Maynotbescanned,copied orduplicated,orposted toapubliclyaccessible
,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l

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website,inwholeorin part. ,l ,l ,l ,l ,l

, Solutionand Answer Guide: StewartKokoska,Calculus:Conceptsand Contexts,5e,2024, 9780357632499,Chapter2:Section Concept Check
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(d) (
f g (f(2)) = f g 22+1
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) (( ,l
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))= f(10(5))= f (50)=502+1=2501
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(e) 1 1 1 1
=  = =
f( g (x)) ,l ,l ,l
f (10x)
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(10x)
2 , l




+1 100x2 +1 , l ,l




1.1.17

The domain of h(x)=
,l ,l , l ,l 4−x2 is−2x2,andtherangeis
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0 y2.Thegraphisthetophalfofacircleofradius2withcenterat the origin.
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1.1.18

Thedomain of ,l ,l f(x)=1.6x−2.4 isall realnumbers.
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1.1.19

t 2 −1
Thedomain of g(t) = ist |t  −1.
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t+1
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1.1.20

x−1
f (x) =
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x −1 isx |x −1,1.
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2
Thedomain of
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
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©2024Cengage. AllRightsReserved. Maynotbescanned,copied orduplicated,orposted toapubliclyaccessible
,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l ,l

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website,inwholeorin part. ,l ,l ,l ,l ,l