Kako najdete mejo (sin ^ 2 (x ^ 2)) / (x ^ 4), ko se x približa 0?

Kako najdete mejo (sin ^ 2 (x ^ 2)) / (x ^ 4), ko se x približa 0?
Anonim

Odgovor:

#1#

Pojasnilo:

Let #f (x) = (sin ^ 2 (x ^ 2)) / x ^ 4 #

#implies f '(x) = lim_ (x do 0) (sin ^ 2 (x ^ 2)) / x ^ 4 #

#implies f '(x) = lim_ (x do 0) (sin (x ^ 2) * sin (x ^ 2)) / x ^ 4 = lim_ (x do 0) {sin (x ^ 2) / x ^ 2 * sin (x ^ 2) / x ^ 2} = lim_ (x do 0) sin (x ^ 2) / x ^ 2lim_ (x do 0) sin (x ^ 2) / x ^ 2 * = 1 * 1 = 1 #