Question

Tolong bantuannya segera pliss dengan caranya y​

Answer 1

Jawab:

limt trigonometrti

i) substitusi nilai variabel

ii) jika hasil  tak tentu , dgn faktor / identitas

Penjelasan dengan langkah-langkah:

5)  lim(x --> π/3)  [ 2x + sin  1/2x ] / [ cos 2x ]

sub x = π/3

L =  [ 2.(π/3)  + sin 1/2 (π/3) ] / [ cos 2 (π/3)]

L =  [ 2π/3  + sin π/6  ] /  [ cos 2π/3 ]

..

sin π/6  = sin 30 = 1/2

cos 2π/3 = cos 120 = - cos 60 =  - 1/2 .

.

L =  [ 2π/3  + sin π/6  ] /  [ cos 2π/3

L =  [ 2π/3 + 1/2  ] / [ - 1/2 ]

L = - 2 [ 2π/3 + 1/2  ]

L = - 4π/3  - 1 atau L = - 1 -  4π/3

.

6)  lim (x-> π)  [ sin x cos x  - sin² x ] /  [ tan x ]

= lim(x ->  π) [ sin x (cos x - sin x)] / (tan x)

= lim(x->  π )  sin x/ tanx . { cos x - sin x}

= lim (x ->  π) cos x - sin x

= cos  π - sin  π

=  -1 - 0

= - 1

.

7) lim(x-> π/4) [  1 - tan x ] / [ sin x - cos x] =

= lim (x -> π/4)  [ cos x ( 1 - sin x/ cos x ) ] /  cos x [ sin x -cos x]

= lim (x -> π/4)  [ cos x - sin x ]/  - cos x [ cos x - sin x ]

= lim(x-> π/4 ) = 1/ (- cos x)

L =  1/cos π/4 =  1/ (1/2 √2)

L =  2/√2 = √2