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Time to conquer Calculus!
Refresh your memory or practice new concepts in calculus with these advanced
problems. TIMETOCONQUERCALCULUS!
TIMETOCONQUERCALCULUS!
TIMETOCONQUERCALCULUS!
TIMETOCONQUERCALCULUS!
Refresh your memory or practice new concepts in calculus with these advanced
Use Photomath to check your answers or to help you work through steps when
Refresh your memory or practice new concepts in calculus with these advanced problems.
you’re stuck. In some cases, you will need to apply multiple math concepts to
Refresh your memory or practice new concepts in calculus with these advanced
Refresh your memory or practice new concepts in calculus with these advanced
problems.
problems.
determine the best or most appropriate solution format. Full solutions are at the
problems. Use Photomath to check your answers or to help you work through steps when
you’re stuck. In some cases, you will need to apply multiple math concepts to
Use Photomath to check your answers or to help you work through steps when
end for your reference.
Use Photomath to check your answers or to help you work through steps when
Use Photomath to check your answers or to help you work through steps when determine the best or most appropriate solution format. Full solutions are at
you’re stuck. In some cases, you will need to apply multiple math concepts to
you’re stuck. In some cases, you will need to apply multiple math concepts to
you’re stuck. In some cases, you will need to apply multiple math concepts to the end for your reference.
determine the best or most appropriate solution format. Full solutions are at
determine the best or most appropriate solution format. Full solutions are at
determine the best or most appropriate solution format. Full solutions are at
the end for your reference.
the end for your reference. the end for your reference.
Question 1. The graph of the following equation
−5
Question 1. The graph of the following equation
Question 1. The graph of the following equation
Question 1. The graph of the following equation y = is concave downward for all values of x
Question 1. The graph of the following equation
−5 x−2
−5 y = −5is concave downward for all values of x
y = is concave downward for all values of x
y =is concave downward for all values of x such that:
is concave downward for all values of such that:
x−2
x−2 x−2
such that:
such that: such that: A. x<0 B. x<2 C. x<5 D. x>0 E. x>2
A. x<0 B. x<2 C. x<5 D. x>0 E. x>2
A. x<0 B. x<2 C. x<5 D. x>0 E. x>2
A. x<0 B. x<2 C. x<5 D. x>0 E. x>2
Question 2. For the following functions, find the
Question 2. For the following functions, find the
domain and/or the yintercept
Question 2. For the following functions, find the
Question 2. For the following functions, find the
Question 2. For the following functions, find the domain and/or the y-intercept.
domain and/or the yintercept √
domain and/or the yintercept 3
domain and/or the yintercept √ A. y = e3x/x− x−7
√ 3x/x− 3√
3x/x− 3
3x/x− 3 A. y = e x−7
A. y = e x−7 A. y = e x−7 B. y = log (5x −2)
3
B. y = log3(5x −2)
B. y = log3(5x −2) B. y = log3(5x −2)
1
TIMETOCONQUERCALCULUS!
Refresh your memory or practice new concepts in calculus with these advanced
problems.
Use Photomath to check your answers or to help you work through steps when
you’re stuck. In some cases, you will need to apply multiple math concepts to
determine the best or most appropriate solution format. Full solutions are at
the end for your reference.
Question 3. Which of the following functions are
QuestioQunQue3ste.stiWoinohni3c.3h.WoWfhthihcihcehofofolfltohtwheiefonfoglllofulwonwicnitngigofunfusnncatcrietoinons saraere
Question 1. The graph of the following equation
QuQuestestioinon3.3.WWhihcihchofotfhtehefofollollwowinigngfufuncntcitoinosnsaraere
continuous for all real numbers x?
QuQueQusteistoenistoni3o.n3W.3W.hiWchhihchoicfhotfhotefhtfoehlfoelofolwloliwlnogiwnifugngfuncfunticnotnciotsnioasnraesraere
continucoocunosntitnfionuruoauoluslsfroefroalralnallulrmeralebalenrsnuumxm?bberesrsx?x?
−5
Question 3. Which of the following functions are
cocnotnitniunouuosusfofroralallrleralealnunmumbebresrsx?x?
y = is concave downward for all values of x
Question 3. Which of the following functions are continuous for all real numbers ?
cocnotcniontnuintoiuunosuuofsourfsoafrollarlrlaelralleralneualnmunbmuembresbrxes?rxs?x?
5
x−2
continuous for all real numbers x?
5 5 5 3
A. y = x
Question 3. Which of the following functions are
5 5
3 3 3
A. y = xA.A.yy==xx
5 5 5 such that:
3 3
A.A.y y==x x
3 3 3 5
A.A.yA.=y =xy =x x
continuous for all real numbers x?
A. y = x3 √
3
A. x<0 B. x<2 C. x<5 D. x>0 E. x>2
√ √√
B. y = 3x−1
3 3 3
5 √√
B. y = B.B.yy==
√√√3x−1 3x3x−−11
3 3 3 3 3
B.B.y y== 3x3x−−1 1
A. y = x3
B.B.yB.=y =y = √
3x3−x3−1x −1 1
B. y = 3 3x−1 3x−1
3x−1 3x3x−−11
√ C.y=
3x3x−−1 1 2
C. y = C.C.yy==
3
3x3−x3−1x −1 1 4x +5
2 2 2
C.C.y y==
B. y = 3x−1
Question 2. For the following functions, find the
4x +54x4x+5+5
C.C.yC.=y =y = 3x−1
2 2
+5+5
2 2 2 4x4x
C. y =
+5+5+5
4x4x4x 2 domain and/or the yintercept
4x +5
C. y = 3x−1 √
2A. y = e3x/x− 3 x − 7
4x +5
A. None of B. A only C. B only
A. NoAneA. . NofNoneoBne. AofofonlyBB. .AAonlyonly C. B onlyCC. .BBonlyonly
A.A. NoNneone ofofB.BA. Aonlyonly C.CB. Bonlyonly
these
A.A.AN.oNneoNneoneof ofBof.BA.BAonly. Aonlyonly C.CB.CBo.nlyBonlyonly
these thtesehese
A. None of B. A only C. B only
thesethtesehese thteseheseB. y = log3(5x − 2)
these D. A, B only E. B, C only F. A, B, and C
A. None of B. A only C. B only
D. A, BD.onlyD.AA, ,BBonlyEonly. B, CEonlyE. .BB, ,CConlyonlyF. A, BF, F.and.AA, ,BCB, ,andandCC
D.D.A,AB, Bonlyonly E.EB. ,BC, Conlyonly F.FA. ,AB, ,Ba,ndandCC
D.D.AD.,AB,ABonly, BonlyonlyE.EB.E,B.C,BConly, Conlyonly F.FA.F,A.B,A,B,a,ndBa,ndaCndC C
these
D. A, B only E. B, C only F. A, B, and C
Question 4. Evaluate each limit:
QuestioQunQue4ste.stiEoivnoaln4u.4at.EeEvalvealacuuathateliemeaceiacth: hlilmimiti:t:
D. A, B only E. B, C only F. A, B, and C
QuQuestestioinon4.4.EvEalvaluatuate eeaceachhlimlimiti:t:
QuQueQusteistoenistoni4o.n4E.4vE.alvEualvatualateuateeaceeacheachlimhliimlti:mit:it:
2
x +5x+6
Question 4. Evaluate each limit:
2 2 2
A. lim
x +5x+6 xx+5+5x+6x+6 2
x→∞
2 2 x −4
Question 4. Evaluate each limit:
A. lim AA. .limlim x +5x +5x+6x+6
2 2 2
x→∞ x→∞x→∞
2 2 2
x xx
−4 −4−4
x +5x x+5x+6x+5+6x+6
A.Alim. lim 2 2
x→∞x→∞
2 x x
A.Alim.Alim. lim −4−4
Question 4. Evaluate each limit:
2 2 2
x→∞x→∞x→∞ x +5x+6
x x x
−4−4−4
A. lim 2
x→∞ x −4 3 3k−5
B. lim
3 3k−5 3 33k3−k5−5
2 k→−1 25k−2
B. lim BB. .limlim 3k−3k5−5
3 3
k→−1 k→−k→−1 1
x +5x+6
25k−2 2525k−k2−2
3k−35k−3k5−5
3 3 3
B.Blim. lim
A. lim k→−k→−1 1
B.Blim.Blim. lim x→∞ x2−4 25k25−k2−2
k→−k→−1k→−1 1 3 3k−5
B. lim 25k25−2k25−k2−2 2
k→−1 25k−2 3x −7x+2
2 2 2 1
C. y = lim
3x −7x+23x3x−7−x7+2x+22
x→
1 1 1 2 2 −6x +5x−1
C. y = limC.C.yy==limlim 3
3x3−x7−x+27x+2
2 2 2
2 2 2
3k−5
x→ 3 x→x→
−6x −6−x6x
+5x−1 +5+5x−x1−1
3x 3−x73x−x+27x−+27x+2
C.C.y y==limlim 1 1
B. lim 3 3 3 2 2
k→−1 x→x→
1 1 1 2 −6−x6x
C.C.yC.=y =limy =limlim 2 2 2 3 3 +5+5x−x1−1
25k−2
x→x→x→ 3x −7x+2
−6x−6x−6x
3 3 3+5x+5−1x+5−x1−1
C. y = lim 1 2
x→3 −6x +5x−1
3x2−7x+2
C. y = lim 1 2
x→3 −6x +5x−1
Question 5. Find the limit
Question 5. Find the limit
Question 5. Find the limit x2 −4
limx→2( )
2
x−2
limx→2(x −4)
x−2
2 2 2 2
2 2 2 2 2
A. 4 B. 0 C. 12 D. 3 E. 2
A. 4 B. 0 C. 1 2 D. 3 E. 2
Question 6. Find the derivative for each of the
following equations
Question 6. Find the derivative for each of the
following equations d
(Hint: Substitute y = with dx in the editing tool on Pho
d
toth to sole the deitie)
(Hint: Substitute y = with dx in the editing tool on Pho
toth to sole the deitie)
A. 2sinx2osx
2
A. 2sinx2osx
B. y = tnx−x
B. y = tnx−x
3 x
C. y = tn
3
C. y = tn x
D. y = 3osx
D. y = 3osx
Question 7. Find the area of the region bounded
by the graphs of y = x2 1, y = −x , x =0and
Question 7. Find the area of the region bounded
x =1 2
by the graphs of y = x 1, y = −x , x =0and
x =1
3
3
Question 5. Find the limit
Question 5. Find the limit
Question 5. Find the limit
Question 5. Find the limit x2 −4 x2 −4
limx→2( x−2 )limx→2( x−2 ) x2 −4
x2 −4 limx→2( x−2 )
limx→2( x−2 )
A. 4 B. 0 C. 1 D. 3 E. 2
A. 4 B. 0 C. 1 D. 3 E. 2
A. 4 B. 0 C. 1 D. 3 E. 2
A. 4B. 0 C. 1 D. 3 E. 2
Question 6. Find the derivative for each of the
Question 6. Find the derivative for each of the
following equationsQuestion 6. Find the derivative for each of the
following equations
Question 6. Find the derivative for each of the following equations
Question 6. Find the derivative for each of the following equations
d d
(Hint: Substitute y = with in the editing tool on Pho
(Hint: Substitute y = with in the editing tool on Pho
following equations
Hint: Substitute in the editing tool on Photomath to solve the derivative
dx dx d
(Hint: Substitute y = with in the editing tool on Pho
toth to sole the deitie)
toth to sole the deitie) dx
(Hint: Substitute y = with d in the editing tool on Pho toth to sole the deitie)
dx
toth to sole the deitie)A. 2sinx2osx
A. 2sinx2osx
A. 2sinx2osx
A. 2sinx2osx B. y = tnx−x
B. y = tnx−x B. y = tnx−x
B. y = tnx−x 3 3
C. y = tn x C. y = tn x
3
C. y = tn x
3
C. y = tn xD. y = 3osx D. y = 3osx
D. y = 3osx
D. y = 3osx Question 7. Find the area of the region bounded
Question 7. Find the area of the region bounded
2 2
Question 7. Find the area of the region bounded
by the graphs of y = x 1, y = −x , x =0and
by the graphs of y = x 1, y = −x , x =0and
Question 7. Find the area of the region bounded by the graphs of
Question 7. Find the area of the region bounded by the graphs of y = x2 1, y = −x , x =0and
x =1 x =1
by the graphs of y = x2 1, y = −x , x =0and
and x =1
x =1
√
√ dy
22 dy
Question 8. If y = ln(x x +1), then =
Question 8. If , then
Question 8. If y = ln(x x +1), then =
dx
dx
3 3
3
3 A. 1+ x 1
2 x B. 1 + √ 1
x +1 x x2+1
A. 1+ x2 +1 B. 1 + √
x x2+1
2 +1 2 +1
2x 2x
C. √ 2+1 D. √ 2+1
2x 2x
x x2+1 x x3+x
C. √ 2+1 D. √ 3+x
x x x x
Question 9. Calculate the derivative:
Question 9. Calculate the derivative:
Question 9. Calculate the derivative:
d √
A. ( 2×sin(3x))
d √
dx (
A. dx 2×sin(3x))
d 2 x
B. ((x −2x+2)e )
d 2 x
dx
B. ((x −2x+2)e )
dx 2
C. d (ln(1+x ))
d 2 2
dx 1+x
C. 1−x
dx(ln(1−x2))
Question 10. Find the following integrals:
Question 10. Find the following integrals:
√ 2 3
7 x−3x −3
A. √ √ 2 dx
7 x−3x −3
4 x
A. π √ dx
3 4 x
B. π 4secθtanθdθ
π
B.−33 4secθtanθdθ
−π
π 3 2x
C. 2 cos( )dx
π
0 32x
C. 2 cos( )dx
0 3
44
5
5
A. 1+ x 1
x2 +1 B. 1 + √ 2
x x +1
2x2 +1 2x2 +1
C. √ 2+1 D. √ 3+x
x x x x
Question 9. Calculate the derivative:
d √
A. dx( 2×sin(3x))
d 2 x
B. dx((x −2x+2)e )
2
C. d (ln(1+x ))
dx 1−x2
Question 10. Find the following integrals.
Question 10. Find the following integrals:
7√ 2
x−3x −3
A. √ dx
4 x
π
B. 3 4secθtanθdθ
−π
3
π 2x
C. 2 cos( )dx
0 3
5
4
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