amxi 221-235
DESCRIPTION
mathTRANSCRIPT
ALGEBRA - clasa a XI - a (simbol AL - XI)
222Culegere de probleme
Analiz matematic XI223
AM - XI. 131 S se afle mulimea soluiilor inecuaiei
a) (-1, 0)
b)
c)
d)
e)
f)
AM - XI. 132 Fie funciile i funciile
. tiind c D1 i D2 sunt domeniile maximede definiie ale celor dou funcii, s se precizeze aceste domenii.
a)
b)
c)
d)
e)
f)
AM - XI. 133 Se consider funciile . tiind c , iar
, s se determine .
a) b) c)
d) e) f)
AM - XI. 134 Cum se poate exprima faptul c graficul unei funcii este simetric fa de punctul C?
a), b),
c), d),
e), f),
AM - XI. 135 Se consider funcia
S se calculeze .
a) 1
b) 2
c) 3
d) 0
e) 1
f) 2
AM - XI. 136 S se calculeze derivata de ordinul unu a funciei
a)
b)
c)
d)
e)
f)
AM - XI. 137 S se calculeze derivata de ordinul doi a funciei
a)
b)
c)
d)
e)
f)
AM - XI. 138 Care este cea mai mic pant posibil a unei tangente la curba ?
a)
b)
c) 1
d) 0
e) 2
f) -3
AM - XI. 139 Fie , .
S se calculeze .
a) nu exist
b)
c)
d)
e)
f)
AM - XI. 140 Fie funcia , .
S se calculeze .
a)nu exist
b) = 1
c) =
d) =
e) = 0
f) =
AM - XI. 141 Fie funcia , unde D este domeniul maxim de definiie al funciei f . S se studieze derivabilitatea funciei f n punctul in caz afirmativ s se calculeze valoarea derivatei n acest punct.
a)= 1
b) =
c) nu exist
d) = 0
e) = 2
f) =
AM - XI. 142 Fie , definit prin . Determinai punctele n care f nu este derivabil.
a) b) c) d) e) f)
AM - XI. 143 Fie , definit prin . Care este
mulimea punctelor de derivabilitate ale funciei f ?
a) R
b) R
c)
d)
e)
f)
AM - XI. 144 Fie irul , cu termenul general ,unde i . Dac , atunci s se determine domeniile decontinuitate C i de derivabilitate D pentru f .
a) b) c)
d) e) f)
AM - XI. 145 Fie , definit prin . S se determine mulimea punctelor n care funcia este derivabil.
a) b) c) d) e) f)
AM - XI. 146 Se d funcia .
S se determine domeniul maxim de definiie E i domeniul su de derivabilitate D .
a) b)
c) d)
e) f)
AM XI. 147 Fiind dat funcia
s se precizeze care din urmtoarele afirmaii este adevrat :
a) f are limit, ;b) f are limit ntr-un numr finit de puncte din Rc) f nu are limit n nici un punct din R ; d) f e continu pe R
e) f are proprietatea lui Darboux pe R ; f) f este derivabil pe R .
AM XI. 148 Fie funciile unde ;
i . S se determine mulimea punctelor de derivabilitate ale funciei f.
a)
b)
c)
d)
e)
f)
AM XI. 149 S se determine derivatele la stnga i la dreapta punctelor x = 0 i
x = 1 ale funciei .
a) b) c)
d) e) f)
AM XI. 150 Se d funcia , definit prin
.
S se determine intervalele i derivata , astfel ca s reprezinte domeniul de derivabilitate al funciei date.
a)
b)
c) d)
e) f)
AM XI. 151 S se gseasc punctele n care funcia ; nu este derivabil.
a) x = 0 i x = 3
b) x = 0 i x = 1
c)
d) f nu este continu pe
e) (0,3)
f)
AM XI. 152 Se d funcia ; s se determine D i mulimea M a punctelor n care f nu este derivabil .
a)
b)
c)
d)
e)
f)
AM XI. 153 Fie funcia
tiind c f este derivabil de ordinul doi pe R s se calculeze f(-2) .
a) 30
b) 30
c) 2
d) 25
e) 15
f) 6.
AM - XI. 154 Se d funcia . S se determinemulimea tuturor valorilor lui m pentru care domeniul maxim de definiie al funcieicoincide cu domeniul maxim de derivabilitate al acestei funcii.
a) b) c) d) e) f)
AM - XI. 155 S se determine parametrii reali a i b astfel nct funcia , definit prin , s fie derivabil pe R .
a)
b)
c)
d)
e)
f)
AM - XI. 156 Fie, definit prin, unde i . Precizai care sunt valorile lui i pentru care f este derivabil pe R .
a)
b)
c)
d)
e)
f)
AM - XI. 157 S se determine parametrii reali a i b astfel nct funcia , definit prin , s fie derivabil pe R .
a)
b)
c)
d)
e)
f)
AM - XI. 158 Fie funcia , .
S se determine constantele reale a i b astfel nct f s fie derivabil pe R .
a)
b)
c)
d)
e)
f)
AM - XI. 159 Pentru ce valori ale tripletului de numere reale funcia
este de dou ori derivabil pe ?
a)
b)
c)
d)
e)
f)
AM - XI. 160 S se calculeze derivata funciei , definit prin
.
a)
b)
c)
d)
e)
f)
AM - XI. 161 S se calculeze derivata funciei , definit prin
.
a)
b)
c)
d)
e)
f)
AM - XI. 162 Fie constante reale nenule cu proprietatea c .
S se determine funciile derivabile pe R astfel nct
pentru oricei, unde b este o constant real.
a)
b)
c) d)
e) f)
AM XI. 163 Fie , unde
i g este derivabil n x = 0 . S se calculeze derivata funciei n x = 0 .
a) nu exist
b) 1
c) 2
d) 0
e)
f) 1
AM XI. 164 Fie funcia , derivabil , cu proprietile : i Determinai i .
a) b) c)
d) e) f)
AM XI. 165 Fie f i g funcii derivabile pe intervalul (-1,1) cu proprietile: , i .
Determinai funcia , definit prin .
a)
b)
c) ;
d)
e)
f)
AM XI. 166 Fiind dat funcia par i derivabil, s se calculeze unde funcia este definit prin relaia :
.
a) b) c) d) e) ;f)
AM - XI. 167 Fie pentru orice i .
tiind c f este derivabil n , s se calculeze .
a) b) c) d) e) f)
AM - XI. 168 Fie , derivabil astfel nct pentru orice . S se calculeze .
a) b) c) d) e) f)
AM - XI. 169 Fie cu proprietatea i pentru care exist .
S se calculeze .
a) 0
b)
c)
d) e) k
f) 1
AM - XI. 170 Fie o funcie derivabil astfel nct , real i
exist . S se calculeze: .
a) 1 b) 0 c) 1 d) a e) a2 f)
AM - XI. 171 Fie o funcie derivabil pe R , cu derivata continu n 1 icu proprietatea c . S se calculeze limita: .
a) b) c) d) e) f)
AM - XI. 172 Se consider funcia . S se determine
, astfel nct funcia , s fieconstant.
a) b) c) d) e) f)
AM - XI. 173 Fie un numr real i funcia dat de:
.
S se determine pentru care f este de dou ori derivabil n .
a) b) c) d) e) f)
AM - XI. 174 S se calculeze derivata de ordinul n a funciei ,
.
a) b) c)
d) e) f)
AM - XI. 175 Fie, i fie irul ,
unde este derivata de ordinul , i . S se calculeze:
.
a) b) c) d) e) f)
AM - XI. 176 S se calculeze
EMBED Equation.2 , pentru funcia ,
.
a)0 b)
EMBED Equation.2 c)
EMBED Equation.2 d)
EMBED Equation.2 e)
EMBED Equation.2 f)
EMBED Equation.2 AM - XI. 177 Fie , definit prin . tiind c
pentru orice , unde i sunt iruri denumere reale , s se stabileasc o formul de recuren pentru i .
(Prin s-a notat derivata de ordinul n a funciei f ).
a)
b)
c)
d)
e)
f)
AM - XI. 178 Se consider funcia , . S se calculeze
.
a) b) c) d) e) f)
AM - XI. 179 Derivata de ordinul n n origine a funciei ,
y = arctg x este:
a) b)
c) d)
e) f)
AM - XI. 180 Fie funcia . S se exprime derivata de ordinul n n funcie de y .
a) b)
c) d)
e) f)
AM - XI. 181 Se d funcia , prin . S se calculeze derivata inversei funciei f n punctul .
a) b) c) d) e) f)
AM - XI. 182 Fie funcia , . S se arate c f este inversabil, s se determine i s se calculeze .
a)
b)
c)
d)
e)
f)
AM - XI. 183 Fie . S se arate c f este bijectiv.Dac g
este inversa lui f , s se calculeze (2) i (2).
a) b) c)
d) e) f)
AM - XI. 184 Fie . S se arate c funcia
este inversabil pe intervalul i fie g inversa lui f .
S se calculeze i .
a) b) c)
d) e) f)
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