Admitere Virtuala
Data: 22 iulie 2002
Ora: 16
00
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1p. (1). Fie sirul ( a
n
) cu termenul general
a
n
=
(
n
2
+ 1
n
2
+ 2
)
n + 1
n + 2
, n
C
N
Alegeti raspunsul corect:
A. lim a
n
= e
n→
∞
B. lim a
n
=
1
n→
∞
e
C. lim a
n
= 1
n→
∞
D. lim a
n
= e
2
n→
∞
E. lim a
n
=
1
n→
∞
2
1p. (2). Fie functia
f: F → R,
F inclus in R, cu valorile:
f( x ) =
x
2
2x
2
– x – 1
Alegeti raspunsul corect:
A. lim f( x ) = –1
x→0
B. lim f( x ) = 1
x→0
C. lim f( x ) =
1
x→0 2
D. lim f( x ) = 2
x→0
E. lim f( x ) = 0
x→0
1p. (3). Primitivele functiei f : ( 0,
∞
) → R,
f(x) = 2x +
ln x
x
sunt functiile F : ( 0,
∞
) → R:
A. F( x ) = 2x
2
+ ln x + C
B. F( x ) = x
2
+ ln
2
x + C
C. F( x ) = x
2
+ xln x + C
D. F( x ) = x
2
+
ln x
+ C
x
2
E. F( x ) = x
2
+
1
(ln x)
2
+ C
2
1p. (4). Primitivele functiei f : R → R,
f( x ) = xe
x
2
sunt functiile F : R → R:
A. F( x ) =
x
2
.e
x
2
+ C
2
B. F( x ) = x·e
x
2
– e
x
2
+ C
C. F( x ) =
x
2
+ e
x
2
–1
. x + C
2
x
2
+ 1
D. F( x ) =
1
.e
x
2
+ C
2
E. F( x ) =
x
2
+ e
x
2
–1
+ C
2
x
2
+ 1
1p. (5). Daca I =
∫
0
1
xe
1–x
dx atunci:
A. I = e
B. I = e – 2
C. I = –2
D. I
<
0
E. I = –e – 1
3p. (6). Fie f : F → R (F fiind domeniul de definitie),
f( x ) = (x + 2)e
1 / x
.
Sa se decida care dintre dreptele de mai jos sunt asimptote ale graficului functiei f.
A. y = 2x
B. x = 1
C. x = 0 si y = x + 3
D. x = –1 si y = 1
E. x = –2 si y = –x
5p. (7). Fie I =
∫
0
1
dx
(x + 1)(x
2
+ 4)
Atunci:
A. I
<
0
B. I =
1
arctg
1
10 2
C. I =
1
( ln
16
– arctg
1
)
10 5 2
D. I =
1
( ln
16
+ arctg
1
)
10 5 2
E. I =
–1
arctg
1
10 2
1p. (8). Fie I =
∫
1
9
1
√
x
dx
Sa se indice raspunsul corect:
A. I = 2
B. I = 2√
2
C. I = 4
D. I =
9
2
E. I = 6
3p. (9). Fie functia
f( x ) =
a
x
– 1
x
, a > 0
Alegeti raspunsul corect:
A. lim f( x ) = 1
x→0
B. lim f( x ) = a
x→0
C. lim f( x ) = ln a
x→0
D. lim f( x ) =
1
x→0 ln a
E. lim f( x ) =
∞
x→0
3p. (10). Fie functia f : (–1, 0) U (0,
∞
) → R cu valorile
f( x ) = e
x
.
ln(1 + x)
x
Alegeti raspunsul corect:
A. lim f(x) = e
x→0
B. lim f(x) = 1
x→0
C. lim f(x) =
1
x→0 e
D. lim f(x) = 2
x→0
E. lim f(x) = e
2
x→0
3p. (11). Primitivele functiei f: (2,
∞
) → R,
f( x ) =
x
2
x
6
– 4
sunt functiile F : (2,
∞
) → R:
A. F( x ) = arc tg x
3
+ C
B. F( x ) = arc sin x
3
+ C
C. F( x ) =
1
ln |x
3
+ 2| + C
3
|x
3
– 2|
D. F( x ) =
1
ln |x
3
– 2| + C
12
|x
3
+ 2|
E. F( x ) = x
3
+ C
x
7
– 4x
3p. (12). Fie I =
∫
0
1
ln(x
2
+ 1)dx. Sa se indice raspunsul corect:
A. I
>
ln2
B. I =
π
+ ln2 + 2
2
C. I =
π
+ ln2 – 2
2
D. I = –
π
+ ln2 + 2
2
E. I
<
0
5p. (13). Fie sirul (a
n
) cu termenul general
S
n
=
1
1·2
+
1
2·3
+
. . .
+
1
n(n + 1)
Alegeti raspunsul corect:
A. lim S
n
= 0
n→
∞
B. lim S
n
= 1
n→
∞
C. lim S
n
=
1
n→
∞
2
D. lim S
n
=
1
n→
∞
3
E. lim S
n
nu exista
n→
∞