Scarica Prove d’esame Matematica generale e più Prove d'esame in PDF di Matematica Generale solo su Docsity!
©L E 2 Y 0 S 2 l 3 P eK`uBtCag QSpoAfZtaweaargeJ PLgLiCk.k R pARlxlK lr\idgkhKtAsr VrLeysPeErlvNePdH.O v FMoaGdweP twTiCtGhQ dIpnffkiRn[iDtyed lPGraeicPailncvuolKuUsa. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 1
Evaluate each indefinite integral.
∫ ( 12 x^2 + 3 ) (^) dx
A) 4 x
+ 3 + C
B) 12 x
+ 3 x + C
C) 4 x
+ 3 x + C
D) None of these
E) 8 x^2 + C
Evaluate each limit.
2) lim
x →^2 −
x − 2
A) ∞ B) −∞
C) 0 D) 4
E) None of these
3) lim
x → 1
f ( x ), f ( x )^ = (^) {
x − 2 , x < 1
− 1 , x ≥ 1
A) 2
B) None of these
C) 9
D) − 1
E) Does not exist.
Evaluate each determinant.
A) 4 B) 0
C) None of these D) − 12
E) 8
Write g ( x )^ (dashed line) in terms of f ( x )
(solid line).
x
y
A) g ( x )^ = − f ( x )^ + 2
B) None of these
C) g ( x )^ = f (− 2 x ) D) g ( x )^ = −
⋅ f ( x ) E) g ( x )^ = − f ( 3 x )
©m i 2 H 0 a 2 w 3 Y BK[uotSai WSloVfYtAwuagrZen dLFLrCc.V [ mA^l[lU drcimgLh[trsJ zr_exsSetrrvfeedj.O p dMpandKeN Xw]iCtAhW hIdncfYiXnSi\tKeI ePhrteJcQaqlOc\u^lQuFsD.
-2- Worksheet by Kuta Software LLC
Solve each equation.
7 n + 6
A) None of these
B)
log 57 3 − 7
C)
log
D)
log 4
E)
log 57
Find the inverse of each function.
- f ( x )^ = − 2 +
x
A) None of these
B) f
− (^1) ( x )^ =
− 10 + 6 x
C) f
− (^1) ( x )^ =
x +
D) f
− (^1) ( x )^ = − 2 −
x
E) f
− (^1) ( x )^ =
− 8 + x
©s l 2 e 0 Z 2 l 3 \ tKVuDtoaD NS]o]fZtywOasrjer FLULaCN.C [ cARltlc mrhi[gXhMtIs` wrPehsVeorYvkendp.d l aMkaqdUed cwciutGhd kIsnAfJiFnRiVt[er FAgltgReibQr]ao K 2 w. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 1
Solve each inequality.
m +
A) m < −
or m > − 2
B) { All real numbers. }
C) None of these
D) m ≥
or m ≤ −
E) m ≥ −
or m ≤ −
Simplify. Your answer should contain only
positive exponents.
kh
j
⋅ h
j
( 2 h^3 j^3 k −^1 )
A)
j^9 k^12
4 h^9
B) 2 h^9 j
C)
8 j^6
h^5 k^18
D)
8 h^6 k^12
j^4
E) None of these
Solve each equation. Remember to check for extraneous solutions.
12) m − 1 = 6 m − 15
A) { 6 } B) { 4 , − 7 } C) None of these D) { 6 , − 7 } E) { 6 , 8 }
©c T 2 C 0 J 2 t 3 v vKruzt]aG pSxoYfqtmwEaIr`eL QL\LyCy.B Q eA\lElb rrVizgghttzsm Er\edsHeirBvsePdY.P c tMvaZdCeV Zwei_tehv ^Ivngfki]nfiptNeP ZCpaql[csugljunsc. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 1
Given the graph of f ( x ), sketch an approximate graph of f ' ( x ).
x
f(x)
A)
x
f '(x)
B)
x
f '(x)
C)
x
f '(x)
D) None of these
©G m 2 D 0 P 2 H 3 y xKLumtTaL _Sfo^fxtrwqaAreeX wLQLWCG.i U YAwlplH jrxilgXhVtxsv vrCeGsoevrwvFeqdl.R \ tMMaNdhey Bwci_tshZ HIYnXfzignsiitweW xPir]eBcoaBlUcvuGlWuvsn. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 2
Solve each inequality.
x + 7
x + 8
A) { 8 } B) (− 8 , − 7 )∪(− 4 , ∞)
C) None of these
D) (− 8 , − 7 )∪[− 4 , ∞) E) {− 8 }
Evaluate each limit.
2) lim
x → 4 +
5 − x + 4
− x + 4
A) − 7 B) − 3
C) − 5 D) None of these
E) − 14
3) lim
x → − 4
x^2
4 x + 16
A) − 6
B) Does not exist.
C)
D) ∞
E) None of these
©I g 2 H 0 E 2 M 3 Z LKtuItJaH XSfohfXtRw\aRrBeQ hLZLKCw.y \ RA\lClS ]riiUguhHt^sq urHeXslefrwvbeMdo.B J zMlaRdCeN XwkiBtehe AINnsfWiNn]idthep xPGrOeHcLajlEcMutlGuvsr.
-2- Worksheet by Kuta Software LLC
Sketch the graph of each function.
- f ( x )^ = (^) { ( x + 1 )
, x < − 1
4 − x
, x ≥ − 1
A)
x
y
B) None of these
C)
x
y
D)
x
y
E)
x
y
Evaluate each determinant.
A) 48 B) None of these
C) − 46 D) − 48
E) 96
Evaluate each indefinite integral.
∫
− 6 x dx
A) − 6 x^2 + C B) 2 x^2 + C
C) − 3 x + C D) None of these
E) − 6 x + C
©o g 2 R 0 L 2 Q 3 u MKxuGtFax MSqoHf\tHwhaHrgef MLELtCI.x I wAtlalg HrmicgrhqtYs^ SrLeNshecrOvZewd[.o A lMxaLdXea GwvintihZ cIjngfsiInzimtEe` NAxlQgBeob[rOag P 2 q. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 2
Simplify. Your answer should contain only
positive exponents.
y
z
( 2 x^4 y^0 z −^4 )
⋅ 2 x
y
z
A) None of these B)
z^9 y
4 x^4
C)
2 z^6 x^4
y^4
D)
8 x^18
y^4 z^19
E)
y^4
zx^2
Solve each equation. Remember to check for
extraneous solutions.
11) − 8 + 6 a = a
A) None of these B) {− 1 , 9 } C) { 2 }^ D) { 2 , 4 }
E) No solution.
Solve each inequality.
b +
A) −
≤ b ≤
B) −
≤ b ≤
C) b ≥
or b ≤ − 1
D) None of these
E) − 1 ≤ b ≤
©H K 2 g 0 \ 2 r 3 W rKKuStOaJ rSGopfvtBwhaprfev gL\LLCR.k f zAZlmlV \rAiOgVhNtfsK BryevsfewrUvteFdf.Q b sM[avdheJ mwBiQtzhz BIhnhfQignCihtPeJ _CXaUl`cyuulhuesZ. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 2
For each problem, determine if Rolle's Theorem can be applied. If it can, find all values of c
that satisfy the theorem. If it cannot, explain why not.
- g ( t )^ =
t^2 + t − 20
t + 6
; [− 5 , 4 ]
A) {− 6 + 2 2 }
B) The function is not continuous on [− 5 , 4 ]
C) {− 6 + 14 }
D) None of these
E) The function is not differentiable on (− 5 , 4 )
©j k 2 0 T 2 v 3 y uKjuEt[aF hSjomfQt_wWaurDew lLbLFCT.A BAdlUlm drriEgLhytvsW erUewspevrovKeBdf.f ^ fMEaqdmeO iwhiDtVhR sIjnTfSitnhiRtweH vPhrjewcdaflhc`ubl[uOs]. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 3
Evaluate each indefinite integral.
∫ (
8 x^3 + 2 x +
35 x
) dx
A) None of these
B) 17 x + C
C) 2 x
+ x
+ 5 x
+ C
D) 8 x
+ 2 x
+ 7 x
+ C
E) 6 x^3 + x + 2 x
+ C
Evaluate each limit.
2) lim
x → − 2 +
4 − x − 2
− x − 2
A) None of these B) − 8
C) 4 D) − 4
E) − 3
Solve each inequality.
x − 3
x − 2
A) None of these
B) ( 1 , 2 )∪( 3 , ∞) C) {− 1 } D) [ 1 , 2 )∪( 3 , ∞) E) { 1 }
Find the inverse of each function.
- f ( x )^ =
x − 1
A) f
− (^1) ( x )^ =
x + 1
B) f
− (^1) ( x )^ =
x − 2
C) None of these
D) f
( x ) (^) =
x + 1
E) f
( x ) (^) = −
x + 1
Evaluate each determinant.
A) 24 B) 27
C) 104 D) None of these
E) − 60
©c j 2 e 0 S 2 O 3 Z AKNuFt\aH nSCoWfgtDwKa]rFeU eLLLNCg.C G jA\lllo irPicguhmtOsx orpeDsFeUrLv[eadk.\ u wMGa[dee_ [wniDtLhp pIUnTfRisnMiNtde[ bPTrCeJcPaZlEcmuYlSumsd.
-2- Worksheet by Kuta Software LLC
Sketch the graph of each function.
- h ( x )^ = (^) {
x − 2 , x < 0
4 − x
, x > 0
A)
x
y
B)
x
y
C) None of these
D)
x
y
E)
x
y
Solve each equation.
4 − 5 x
A)
log 68
B)
− log 9 18 − 5
C) None of these
D)
log 4
E)
− log 4
©M u 2 W 0 W 2 E 3 r xKPuMtfaw USSoofBtrwxaLrUer ELOLxC^.B L tALlPlA ZrFi\g`hAtxsq NrPebsSeIrGv_ead[.O X VMxandiee mwSiVtuhA QILnufFi]njibtyei OArlxgje[bqrfai Y 2 e. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 3
Solve each equation. Remember to check for
extraneous solutions.
- − 2 + ( 8 − x )
= ( 4 − x )
A) { 4 , 9 }^ B) None of these C) { 4 , − 5 }^ D) { 4 , − 9 } E) { 4 }
Simplify. Your answer should contain only
positive exponents.
- (^) (
2 xy
z
⋅ x
y
z
2 zy
3 )
A)
x^12
z^15 y^3
B)
z^4
x^6 y^4
C)
x^7
4 y^6 z^15
D)
8 z^10
y^2
E) None of these
Solve each inequality.
m − 1 ≥ −
A) m ≥
or m ≤
B) { All real numbers. }
C) m ≤ − 3 or m ≥
D) m ≤
or m >
E) None of these
©V B 2 t 0 j 2 u 3 L YKpuotUah GSWoqfjtswTahrxeB TLFLCCa.Y o YA[l[l[ oryiAgwhotrsW \rNeTsvebruvZeGdk.V GMaasdeL PwNiVtnhP cIJnxfuiFndivtees JCuaLlRcDuBlpucsa. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 3
Given the graph of f ( x ), sketch an approximate graph of f ' ( x ).
x
f(x)
A)
x
f '(x)
B)
x
f '(x)
C) None of these
D)
x
f '(x)
Find the intervals on which each function is
continuous.
- f ( x )^ = (^) {
− x^2 + 2 x + 1 , x ≠ 2
2 , x = 2
A) (−∞, 2 ), ( 2 , ∞)
B) (−∞, 1 ], ( 1 , ∞)
C) None of these
D) (−∞, 3 ], ( 3 , ∞)
E) (−∞, ∞)
©g c 2 n 0 w 2 b 3 u \KeuYtsaV USYosfFtmwga]rkeG BLJLXCD.J M bAklkl_ ]r`iygMhItIsX QrLeys[eArEvBehd].N I vMAaMd\eR xwjirtsh_ cIrnwf\iHnqiDtfeF WPSrHetc_aVlgcFuflDuUsV. Worksheet by Kuta Software LLC
Matematica Generale
Prova Scritta
Nome___________________________________ ID: 4
Find the inverse of each function.
- g ( x )^ = x + 1
A) g
− (^1) ( x )^ =
− 5 x + 20
B) g
( x ) (^) = − 3 x + 9
C) None of these
D) g
− (^1) ( x )^ =
7 x − 2
E) g
− (^1) ( x )^ = x − 1
Evaluate each limit.
2) lim
x → (^2) (
2 e
x − 2
e
x − 2
)
A) Does not exist. B) 10
C) None of these D) 3
E) 6
Write g ( x )^ (dashed line) in terms of f ( x )
(solid line).
x
y
A) None of these
B) g ( x )^ = −
⋅ f ( x ) C) g ( x )^ = 3 f (− x ) D) g ( x )^ = f (^) (−
x ) E) g ( x )^ = − f ( 3 x )
Solve each equation.
2 − 2 p
A)
− log 57
B)
− log 16 11 + 2
C)
log 2
D)
− log 16
E) None of these
Evaluate each determinant.
A) − 56 B) 56
C) None of these D) − 48
E) − 8
Solve each inequality.
x + 8
x + 7
A) (−∞, − 8 )∪(− 7 , 8 ] B) (− 8 , − 7 )∪( 8 , ∞) C) (−∞, − 8 )∪(− 7 , 8 )
D) None of these
E) (− 8 , − 7 )∪[ 8 , ∞)
©` ^ 2 m 0 L 2 m 3 p YKjuotDaV jSioSfQtlwnaKrme] QLuLLCj.h j HAMlwlm UrDiLgUhgtLsi TrSeHsSedrEvdeTdp.B n HMKaLdCeb ewwilt^hf ZILnxfoiBn\iStHec mPjrSeZcQaplwcfuIlhuxsH.
-2- Worksheet by Kuta Software LLC
Evaluate each limit.
7) lim
x → 3
x
A) −
B) −∞
C) ∞ D) − 6
E) None of these
Sketch the graph of each function.
- h ( x )^ =
2 , x < − 2
− x − 1 , − 2 ≤ x ≤ 4
x − 3
, x > 4
A)
x
y
B) None of these
C)
x
y
D)
x
y
E)
x
y
Evaluate each indefinite integral.
5 dx
A) 10 x + C B) 5 x + C
C) C D) 4 x + C
E) None of these
