Misal diberikan lim_(x→∞) f(x) = 9 dan lim_(x→∞) g(x) = 12 dan lim_(x→∞) h(x) = 8. Hitunglah nilai limit fungsi berikut: a. lim_(x→∞) [f(x) + g(x) - h(x)] b. lim_(x→∞) [(f(x)·h(x))/g(x)] c. lim_(x→∞) [2h(x) - √(f(x)/g(x))]²

Question

Jawaban :

a. 13

b. 27/2

c. 1.027/4 - 16√3

Ingat!

Jika lim(x->c) f(x) ada dan lim(x->c) g(x) ada , maka

>> lim(x->c) [f(x) ± g(x)] = lim(x->c) f(x) ± lim(x->c) g(x)

>> lim(x->c) f(x).g(x) = lim(x->c) f(x) . lim(x->c) g(x)

>> lim(x->c) f(x)/g(x) = [lim(x->c) f(x)] / [lim(x->c) g(x)]

>> lim(x->c) (f(x))² = [lim(x->c) f(x))²

>> lim(x->c) √(f(x)) = √(lim(x->c) f(x))

Diketahui

lim(x→∞) f(x) = 9

lim(x→∞) g(x) = 12

lim(x→∞) h(x) = 8

Sehingga

a. lim(x→∞) [f(x) + g(x) - h(x)]

= lim(x→∞) f(x) + lim(x→∞) g(x) - lim(x→∞) h(x)

= 9 + 12 - 8

= 21 - 8

= 13

b. lim(x→∞) [(f(x)·h(x))/g(x)]

= [lim(x→∞) f(x) . lim(x→∞) g(x)]/[lim(x→∞) h(x)]

= (9 . 12)/8

= 108/8

= 27/2

c. lim(x→∞) [2h(x) - √(f(x)/g(x))]²

= [2 lim(x→∞) h(x) - √(lim(x→∞) f(x))/(lim(x→∞) g(x)))]²

= [2 . 8 - √(9/12)]²

= [16 - √(3/4)]²

= [16 - √3/2]²

= 256 - 16√3 + 3/4

= 1.027/4 - 16√3

Dengan demikian diperoleh

a. lim_(x→∞) [f(x) + g(x) - h(x)] = 13

b. lim_(x→∞) [(f(x)·h(x))/g(x)] = 27/2

c. lim_(x→∞) [2h(x) - √(f(x)/g(x))]² = 1.027/4 - 16√3

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