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x→0x
x= 1
x→0ex−1
x= 1.
x→1x2−1
2x2−x−1
x→∞
!x3
x2+1− x
"
x→8
√9+2x−53√
x−2
x→2
#1
x2−2x− x
x2−4
$
x→1x100−2x+1x50−2x+1
x→1x+x2+x3+...+xn−n
x−1.
x→0(1+x)(1+2x)...(1+nx)−1
x
x→0(1+mx)n−(1+nx)m
x2
x→2(x2−x−2)20
(x3−12x+16)10.
x→∞ x43
#3√
x2 + 1 − 3√
x2 − 1$
x→16
4√
x−2√x−4
x→∞√
x3#√
x + 1 +√
x − 1 − 2√
x$
x→a+
√x−
√a+
√x−a√
x2−a2 .
x→0x
x
x→0x
x
x→ax− ax−a
.
x→a
1x− 1
a
x−a
x→0
√x− 3
√x
2 x
x→0
√1− x2
1− x
x→01− x 2x 3x
1− x.
x→0( ax)( bx)
x→aa x− x a
x−a
x→1(1 − x) x 2.
x→∞!1 − 1
x
"x
x→π2( x) x
x→0
!1+ x1+ x
" 1x
x→∞!
x+ax−a
".
x→∞e1+ x
(e3x+e−3x)
x→4x2+7x−44x2−6x+8
x→2x−2√x+2−2
x→0x2 ( 1
x2 )
x
x→∞!
1−2x5−2x
"x.
x→10x− 10
10x
x→0+
!1+x2+x
" 1−√
x1−x
x→1
!1+x2+x
" 1−√
x1−x
x→−∞(#
9x2 + (2x − 1) −#
9x2 − (2x − 1))
x→∞1√
9x+2x2−x√
2.
x→∞(x2−x+1)(x10+x+1)
x→−1
$2x
π+ x
%.
x→−1x3+1(x+1)
x→0 x · e x−11− x
x→2x− 3x
x2
x→π6
2 2 x+ x−12 2 x−3 x+1
.
x→0( 3x− x)(e4x2−3x+1−e)
((x+1)(2x+1)(3x+1))(√
x3+6x+4−2)
x→0( 3x− x)(22−22(x+1))
((x+1)(3x+1)(5x+1))(√
x3+x2+9−3).