1 limit fungsi [tex]1 \: \frac{lim}{x - > 1 } \: \: \: \: 7x \sqrt{2x - 1} \\ \\ 2 \: \: \frac{lim}{x - > 0} \: \: \: \: \frac{ \sin(2x) }{ \sin(8

jawab

1. limit (x ->1) 7x √(2x - 1)
subx = 1--> 7(1) √(2.1-1) = 7√1 = 7

2. limit (x -> 0)  (sin 2x)/ (sin 8x)
= 2x/8x
= 1/4

3. limit (x ->0) (tan x - sin x)/(x³) = 

= sin x/ cosx  - sin x / (x³)
= (sin x - sin x cos x) / (x³. cos x)
= sin x (1 - cos x) / (x³. cos x)
= sin x (1 - (1 - 2 sin² ¹/₂ x)) / (x³. cos x)
= sin x (2 sin² ¹/₂ x) / (x³. cos x)
= x(2)(1/2 x)(1/2 x) /x³ . 1/cos x
= 1/2 x³/x³.  (1/cos x)
= 1/ (2 cos x)
x= 0
limit  = 1/ 2 cos.0 = 1/2