HW 2 – 6: Special Trig Limits
Math 400
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lim sin u
lim
u
=
= 1 where u is some f (x)
x→ 0 u
x → 0 sin u
1.
lim sin(5x)
!
x→ 0
5x
2.
lim −2sin(3x)
!
x→ 0
3x
3.
lim
2x
x → 0 sin(2x)
!
4.
lim sin(5x)
!
x→ 0
5
5.
lim
5
!
x → 0 sin(5x)
6.
lim
sin(2x)
x → 0 3sin(x)
7.
lim sin(6x)
!
x→ 0
3x
8.
lim sin(4 x)
!
x → 0 sin(8x)
9.
lim sin 3 (2x)
x→ 0
x3
Math 400 HW 2 – 6 !
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10.
lim
4x3
!
x → 0 sin 3 (4 x)
11.
lim
25
!
2
x → 0 sin (5x)
12.
lim sin 2 (2x)
x → 0 24 x 2
lim 1− cos(ax)
lim cos(ax) − 1
=
= 0 where a non zero real
x→ 0
x→ 0
ax
ax
13.
lim 1− cos x
!
x→ 0
2x
14.
lim cos 3x − 1
!
x→ 0
2x
15.
lim
3 − 3cos(2x)
x→ 0
2x
Mixed Practice
lim
x +1
16.
!
x → 0 cos x
Math 400 HW 2 – 6 !
lim 2tan 2 (x)
17.
!
x→ 0
x
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18.
lim
3sin x
x→ 0
x3
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19.
lim 1− cos 4x
!
x→ 0
sin5x
lim 1− cos3x
22.
!
x→ 0
sin2x
20.
lim
cos2x
!
x → 0 sinx + 2
lim 3 + cos3x
23.
!
x → 0 sin x + 1
21.
lim
sin2x − 2
x → 0 2cos x + 1
lim 1− cos2 x
24.
x → 0 1− cos x
!
Limits involving Vertical Asymptotes of the trigonometric functions
25.
lim
π + tan (x)!
x→
2
26.
lim
π − tan (x)!
x→
2
lim
27. x → π tan (x)
2
28.
lim
cot (x) !
x → π+
29.
lim
cot (x)!
x → π−
30.
Math 400 HW 2 – 6 !
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lim
cot (x)
x→π
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lim
π + sec (x) !
31.
x→
2
lim
π − sec (x)!
32.
x→
2
lim
33. x → π sec (x)
2
34.
lim
csc (x) !
x → 2π +
35.
lim
csc (x)!
x → 2π −
36.
lim
csc (x)
x → 2π
37.
lim
tan 2 (x)!
x → 2π
38.
lim
sec 2 (x)!
x → π /2
39.
lim
− cot (x)
x→π
40.
lim
cos (x) !
x →−∞
41.
lim
sin (x)!
x → +∞
42.
lim
− cot (x)
x→ ∞
Math 400 HW 2 – 6 !
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© 2016 Eitel