Limits

Malang Study Club

1. Find the limit of the functions below! a.

lim x →3

b. lim x →0

c.

lim x→∞

x 2 -x-6

d.

4- 5x + 1

lim

( y − 2)→ 0

3x

4

9+x − 9−x

e.

lim

d.

lim

x →1

x + 5 + 2x-1

1 ⎛ 1 2 ⎞ − ⎜ ⎟ y-2 ⎝ 2y 2 -y-3 y 2 + y ⎠

x − 3

3

x

x −1

2. Find the limit of the functions below! a.

lim x →0

1-cos 2x 1 x ⋅ tan x 2

x→

b. lim sin 3x − sin 3x .cos 2x x →0 2x 3 c.

π

2

e. lim x →0

cos 3x - cos x sin 2x . cos 2x

sin 2x 3 − 2x + 9

1 − cos2 (x-2) x → 0 3 x 2 − 12 x + 12

lim

3. Find the limit of the functions below! a.

⎛ 1⎞ lim ⎜ 1 + ⎟ x →∞ ⎝ x⎠

x +5

d.

⎛ x +3⎞ b. lim ⎜ ⎟ x →∞ ⎝ x − 1 ⎠

⎛ x +1 ⎞ lim ⎜ ⎟ x →0 ⎝ 2 x + 3 ⎠

x +1

1

x

⎛ x 2 + x + 1 ⎞ 2 x +1 e. lim ⎜ 2 ⎟ x →∞ x + 2 x − 2 ⎝ ⎠

1

c.

lim (1 + 2 x ) x x →0

4. Find the lim

f ( x + h) − f ( x ) h

h→0

from the functions below!

a. f(x) = sec x b. f(x) = cosec x c. f(x) =

4

x3

d. f(x) = x − 2 x e. f(x) = (x2 – 3)(x – 3)2

Latihan Matematika SMA XI IPA

Limits