tugas

1. 6. 𝑔( 𝑥) =
√ 𝑥−5
𝑥−5
𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 3
Lim
𝑥=3
√ 𝑥−5
𝑥−5
= lim
𝑥=3
√ 𝑥−5
𝑥−5
×
𝑥+5
𝑥+5
= lim
𝑥=3
(√ 𝑥−5)( 𝑥+5)
𝑥2−25
=
(√3−5)(3+5)
32−25
=
8√−2
−16
7. 𝑔( 𝑥) =
√ 𝑥−5
𝑥+2
𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 8
Lim
𝑥=8
√ 𝑥−5
𝑥+2
= lim
𝑥=8
√ 𝑥−5
𝑥+2
×
√ 𝑥+5
√ 𝑥+5
= lim
𝑥=8
𝑥−25
( 𝑥+2)(√ 𝑥+5)
=
8−25
(8+2)(√8+5)
=
−17
30√2
8. ℎ( 𝑥) = 5𝑥2 − √ 𝑥 + 7 𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 5
lim
𝑥=5
5𝑥2 − √ 𝑥 + 7 = 5(5)2 − √5 + 7 = 132 − √5
9. 𝑓( 𝑥) =
𝑥−6
𝑥−2
𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 6
Lim
𝑥=6
𝑥−6
𝑥−2
=
6−6
6−2
=
0
4
= 0
10. ℎ( 𝑥) =
( 𝑥−𝑎)2+𝑥−6
𝑥−𝑎+3
𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 𝑎
lim
𝑥=𝑎
(𝑥−𝑎)2+𝑥−6
𝑥−𝑎+3
= lim
𝑥=𝑎
𝑥2−2𝑎𝑥+𝑎2+𝑥−6
𝑥−𝑎+3
=
𝑎2−2𝑎2+𝑎2+𝑎−6
𝑎−𝑎+3
=
𝑎−6
3

2. 1. 𝑓( 𝑥) = 5(tan 3𝑥) 𝑑𝑖𝑚𝑎𝑛𝑎 𝑎 𝑎𝑛𝑔𝑘𝑎 𝑟𝑒𝑎𝑙 𝑐
lim
𝑥=0
5(tan 3𝑥) = lim
𝑥=0
5 .
tan 3𝑥
3𝑥
= 5 .1 = 5
2. ℎ( 𝑥) = tan 𝑥 + cos(3𝑥 − 1) 𝑑𝑖𝑚𝑎𝑛𝑎 𝑐 = 4
3. 𝑓( 𝑥) =
5𝑥3+2𝑥
cos𝑥
+ √𝑥34
− tan 𝑥 .sin 𝑥 , 𝑑𝑖𝑚𝑎𝑛𝑎 𝑐 = 5
4. 𝑡( 𝑥) = cos√5𝑥 − 3 + tan 𝑥, 𝑑𝑖𝑚𝑎𝑛𝑎 𝑐 =
𝜋
2
5. ℎ( 𝑥) = √8𝑥25
− 4 sin 𝑥 + 13 , 𝑢𝑛𝑡𝑢𝑘 𝑥 > 1
6. 𝑔( 𝑥) =
11𝑥2−8𝑥+9
sin𝑥
𝑜𝑛 𝑡ℎ𝑒 𝑟𝑒𝑎𝑙 𝑙𝑖𝑛𝑒
lim
𝑥=0
11𝑥2 − 8𝑥 + 9
sin 𝑥
= lim
𝑥=0
𝑥
sin 𝑥
.11𝑥2 − 8𝑥 + 9 = 9
7. 𝑣( 𝑥) = sin 𝑥 + cos 𝑥 𝑜𝑛 𝑡ℎ𝑒 𝑟𝑒𝑎𝑙 𝑙𝑖𝑛𝑒
lim
𝑥=0
sin 𝑥 + cos 𝑥 = sin 0 + cos0 = 0 + 1 = 1
8. 𝑡( 𝑥) = 𝑠𝑖𝑛2 𝑥+ 𝑐𝑜𝑠2 𝑥 , 𝑑𝑖𝑚𝑎𝑛𝑎 𝑐 =
𝜋
2
9. 𝑓( 𝑥) =
𝑡𝑎𝑛𝑥
𝑠𝑖𝑛𝑥
, 𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 2𝜋 𝑑𝑎𝑛 𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 6𝜋
lim
𝑥→0
tan 𝑥
sin 𝑥
= lim
𝑥→0
tan 𝑥
𝑥
.
𝑥
sin 𝑥
.
𝑥
𝑥
= 1 × 1 × 1 = 1
10. 𝑔( 𝑥) = √ 𝑥 − 15 + sin 𝑥 − 10 , 𝑑𝑖𝑚𝑎𝑛𝑎 𝑥 = 11