Paano mo nahanap ang limitasyon ng (kasalanan (7 x)) / (kayumanggi (4 x)) bilang x approaches 0?

Paano mo nahanap ang limitasyon ng (kasalanan (7 x)) / (kayumanggi (4 x)) bilang x approaches 0?
Anonim

Sagot:

7/4

Paliwanag:

Hayaan #f (x) = sin (7x) / tan (4x) #

#implies f (x) = sin (7x) / (sin (4x) / cos (4x)) #

#implies f (x) = sin (7x) / sin (4x) * cos (4x) #

#implies f '(x) = lim_ (x to 0) {sin (7x) / sin (4x) * cos (4x)} #

#implement f '(x) = lim_ (x to 0) {(7 * sin (7x) / (7x)) / (4 * sin (4x) / (4x)) * cos (4x)

#implement f '(x) = 7 / 4lim_ (x to 0) {(sin (7x) / (7x)) / (sin (4x) / (4x)) * cos (4x)} = 7/4 {lim_ (x to 0) sin (7x) / (7x)) / (lim_ (x to 0) sin (4x) / (4x)) lim_ (x to 0) cos (4x) = 7/4 * 1/1 * cos (4 * 0) = 7/4 * cos0 = 7/4 * 1 = 7/4 #