Limit Fungsi, ada/tidak ada?

lim cot(θπ) sin(θ) / (2 secθ)

θ->0

Lim sin(θ) / (2tan(θπ) sec(θ)

θ->0

Lim (sin(θ) / sec(θ)) (1/(2tan(θπ) )

θ->0

(1/2) lim (θ->0) tan(θ)/ tan(θπ)

= (1/2)(1/π)

= 1/(2π)

ingat bahwa:

lim (x->0) tan(x)/ tan(ax) = 1/a

.

...

lim....cot(πθ) sin(θ)

θ→0 --------------------

............2 sec(θ)

lim.....1.............sin(θ)

θ→0 ------------...---------------

........tan(πθ)....2 1/cos(θ)

lim.....1...........1

θ→0 ------------...-- sin(θ) cos(θ)

........tan(πθ)....2

lim.....1...........1

θ→0 ------------...-- ½ sin(2θ)

........tan(πθ)....2

lim...sin(2θ)

θ→0 ------------ ¼

........tan(πθ)

2....1

---..---

π....4

.1

----

2π

Kita periksa dan lihat grafiknya di sini ↓

http://www.wolframalpha.com/input/?i=lim%28cot%28t...

Jadi limit fungsi yang diberikan ADA.

Ok.

limθ->0 [(cot θπ)*sin(θ)]/(2 sec θ)

dipecah pecah dulu :

cot θπ =(cos θπ)/(sin θπ)

sec θ = (1/cosθ)

jadi di tulis aja bgini :

[(cot θπ)*sin(θ)]/( sec θ) = [cosθπ sinθπ]/ [sinθπcosθπ] corat- coret

jadi sin θ/sinθπ

karena sec θ = (1/cosθ)

maka 2 sec θ = 2(1/cosθ)

jadi limθ->0 [(cot θπ)*sin(θ)]/(2 sec θ) = limθ->0 sin θ/2sinθπ corat coret

1/2π

lim cot(θπ) . sin(θ)

θ->0 ──────────

2 . sec θ

. lim [1/tan (θπ). sin(θ)] /(2 ./cos (θ))

= θ->0

lim [sin(θ)cos(θ)] / [2 tan(θπ)]

=θ->0

lim sin 2(θ) / 4 tan(θπ) = 2/4π = 0,5/π ..............................(jwbanny)

=θ->0

jika ada, hasilnya bisa didapat

jika tidak ada, hasilnya tidak bisa didapat, kalau bahasa kalkulator "error"

contoh nya : lim 1/x = 1/0 = tak hingga (ga ada artinya)................

x>0