QUIZZZ
Tentukan hasil dari
[tex]\boxed{\displaystyle\sf\lim_{x\to16}\:\frac{x-\sqrt{x}-12}{4-\sqrt{x}}}[/tex]
a. -7
b. 5
c. 7
d. 3
e. -5
Tentukan hasil dari
[tex]\boxed{\displaystyle\sf\lim_{x\to16}\:\frac{x-\sqrt{x}-12}{4-\sqrt{x}}}[/tex]
a. -7
b. 5
c. 7
d. 3
e. -5
Verified answer
Materi : Limit Fungsi
[tex][tex]\boxed{\displaystyle\sf\lim_{x\to16}\:\frac{x-\sqrt{x}-12}{4-\sqrt{x}}}[/tex][/tex]
Aturan L'Hopital ( Turunannya )
Lim ( x => c ) f(x)/g(x) = Lim ( x => c ) f'(x)/g'(x)
____________________________/
( x - x¹/² - 12 )/( 4 - x¹/² )
---
f(x) = x - x¹/² - 12x⁰
f'(x) = ( 1.1 )x⁰ + ( -1.½ )x-¹/² + ( -12.0 )x-¹
f'(x) = 1 - ½x-¹/²
f'(x) = 1 - ½/√x
f'(x) = √x/√x - ½/√x
f'(x) = ( √x - ½ )/√x
---
g(x) = 4x⁰ - x¹/²
g'(x) = ( 4.0 )x-¹ + ( -1.½ )x-¹/²
g'(x) = - ½x-¹/²
g'(x) = - ½/√x
---
Langsung Saja
Lim ( x => 16 )
f'(x)/g'(x)
= ( [ √x - ½ ]/√x )/( -½/√x )
= ( √x - ½ )/√x . √x/(-½)
= ( √x - ½ ) . 1 ÷ (-½)
= ( √x - ½ ) . ( -2 )
= - 2√x + 1
Maka masukin nilai ( x = 16 )
= - 2 . √16 + 1
= - 2 . 4 + 1
= - 8 + 1
= -7
Semoga bisa membantu
[tex] \boxed{ \colorbox{darkblue}{ \sf{ \color{lightblue}{ answered\:by\: BLUEBRAXGEOMETRY}}}} [/tex]
Penyelesaian
[tex]{\displaystyle\sf\lim_{x\to16}\:\frac{x-\sqrt{x}-12}{4-\sqrt{x}}}[/tex]
.
Gunakan teorema L'Hopital, turunannya:
[tex] \frac{x - x {}^{ \frac{1}{2} } - 12}{4 - {x}^{ \frac{1}{2} } } [/tex]
Anggap itu f(x)/g(x), sehingga hasilnya f'(x)/g'(x) yaitu:
1-½/√x / -½/√x
Jadi tinggal substitusikan
=1-½/√16 / -½/√16
=1-½/4 / -½/4
=4(1-½/4)/-½
=4-½/-½
=3½/-½
=-7(a.)
Semoga bermanfaat