Calculus Exercises Limits

Exercises : Limits



① Iim
-72
9+2

y y2t5yt6

lim lim
lim Y +2
=
y→zYty→z 2


¥7259 y' ¥36
-72 ≥
y y2t5yt6 limy
y -72
+ +


2 t 2
=



(272+512)+6
=
4

20
= I

5


{info (22-8)%3

Iim (22-8)%3=3 {17022 ¥708 -




2-70
=
2103-8

=
✓ -8

= -2




⑤ Iim
✗ → -3
2+3

x2 +421-3

Iim Kt3 / Im CKt3)
=
✗ → -3 n→ -3
✗ 2+4×+3 ( ✗ + 1) (Rts )
Iim 1
=

n→ -3
zetl

I
=



-3+1
I
=
_




2




④ Iim
n→z
R2 -

7kt / 0

N -

2

tim x2 -7N +10 ( N -
5) ( N -

2)
Ijm
=
N -72 N -72
z -
z ok -2


=%zN -5
= 2-5

=-3




?⃝

, ⑤ Iim
t -7-1
t2t3tt2
-12 -

t -
2


Iim
1-2+31-+2
iim
It + 1) (1-1-2)
=

1-
2) ( ttl )
→ -1 t -7-1
t2 -
t -2 It -




Iim tt2
=

t→ -1
t -
2

-11-2
=


-

I -2

l
= -




3




593+892
⑥ Iim
y -70 3y4 -1692
Iim 593+892 / im 92154+8 )
=

"→° y -70
344-1692 y2( 392-16 )
Iim 591-8
=
y -70
zyz-16
=
51071-8
31072-16
l
= -




2




I 1

it
③ Iim a- Ntl
→◦
K

I ' ✗ title -1
t
Iim " l Ntl In 1) Catt )
-



Iim
-




=
a -70 a -70
x a



n→0&n-Dcn+D £]
Iim 22
=
✗


2
tim
=

a -70
( a- DINH )

2
=


Co -
1) (01-1)
= -2




⑧ Iim
V3 _
8
v -72
v4 -16

Iim v3 -8 ' im (V -
2) ( V72 ✓ + 4)
=
✓→ 2 ✓→ 2
v4 -16 ( ✓ 2+4 )( ✓ 1- 2) ( V 2) -




Iim VZTZV +4
=

v -72
( ✓ 2+4)CVt2)
=
(2721-212)+4
(221-47121-2)
3
=

-8