2100419923

2. Obliczyć granice ciągów:

(2.7) On (2.9) a.

(2.11) a„ = i/5ńT3

’13)“" = (l ⁺ D

>/3" + 4"	(2.2) a„ = >/5^n + 6"
V3 ■ 2" + 2 • 3"	(2.4) a., = {/9 • 7" + 7 ■ 8"
i/2" + 5" + 9"	(2.6) a„ = V3- 7" +8" + 3-11"
W*(!)■*(:	!)' M-©'*©'*©
	(2.10) o„ = \/23n

(2.

(2.15) a

(2.19) a„ (2.21) a„

5n+4

_ /2n + 5\⁴ⁿ⁺³ "l 2n /

—eE-r

4n+7

(2.12) a„ = V7n + 9 (2.14) o„ '• ^3X (2.16) a„

(2.18) a„

(2.20) a„

/*

(2.22) o„ =

(2.24) m,

Cr²) (^f f—V

\ n² + 2 /

'3n + 5\ x 3n ) _Ą

- f³ⁿ ~ ²\^w

V 3n /_a

(2.26) o.= (2±»)^

’+l

3n+2

3) Obliczyć granice funkcji

—    4x

(3.1) lim

i-»o x³ + 2x

(3.3) lim ——7-^v ' *-»3 x² - 9

-    16

(3.5) lim-—

^v ' *-*2 x — 2

(3.7) lim

..    3x² + 5x

(3.2) lim —7-

^v ’ x-»o Zr³ - x

(3.4) lim ---7

^{v 7} *-*2 x - 2 x⁴ - 1

⁽³-⁶⁾I^7TT

(3.8) lim

(3.9) lim ^y/l+l 1    (3.10) lim

^V    ’ x—*0    T    ^v    ' I-łO

(3.11) lim

^{V    ,} X—fl

3x

__    \Ąr + 4 - 2

(3.12),im

r - 1 ^v ' x-2 x - 2

13