Domanda n. 3dd7c

Domanda n. 3dd7c
Anonim

Risposta:

= - 2csc2xcot2x =2csc2xcot2x

Spiegazione:

Permettere

f (x) = csc2x f(x)=csc2x

f (x + DeltaX) = csc 2 (x + DeltaX)

f (x + DeltaX) -f (x) = csc 2 (x + DeltaX) -csc2x

Adesso, lim ((f (x + DeltaX) -f (x)) / ((x + DeltaX) -Deltax)) = (csc 2 (x + DeltaX) -csc2x) / (DeltaX)

= 1 / (DeltaX) ((csc 2 (x + DeltaX) -csc2x) / (DeltaX))

= 1 / (DeltaX) (1 / sin (2 (x + DeltaX)) - 1 / sin (2x))

= 1 / (DeltaX) ((sin2x-sin2 (x + DeltaX)) / (sin (2 (x + DeltaX)) sin2x))

SINC-Sind = 2cos ((C + D) / 2) sin ((C-D) / 2)

implica

C = 2x, D = 2 (x + Deltax)

(C + D) / 2 = (2x + 2 (x + Deltax)) / 2

= (2x + 2x + 2Deltax) / 2

= (4x + 2Deltax) / 2

= 2 (2x + DeltaX) / 2

(C + D) / 2 = 2x + DeltaX

(C-D) / 2 = (2x-2 (x + Deltax)) / 2

= (2x-2x-2Deltax) / 2

= (- 2Deltax) / 2

(C-D) / 2 = -Deltax

Sin2x-sin2 (x + DeltaX) = 2cos (2x + DeltaX) sin (-Deltax)

lim (Deltaxto0) ((f (x + DeltaX) -f (x)) / ((x + DeltaX) -Deltax)) = 1 / (DeltaX) (2cos (2x + DeltaX) sin (-Deltax)) / (sin (2 (x + DeltaX)) sin2x)

= (2) (- sin (DeltaX) / (DeltaX)) (1 / sin (2x)) ((cos (2x + DeltaX)) / (sin (2 (x + DeltaX))))

(- 2) / sinxlim (Deltaxto0) (sin (Deltax) / (Deltax)) lim (Deltaxto0) ((cos (2x + Deltax)) / (sin (2 (x + Deltax)))))

lim (Deltaxto0) (sin (DeltaX) / (DeltaX)) = 1

Adesso, = - 2cscx (1) (cos2x) / sin (2x)

= - 2csc2xcot2x