Calculo Diferencial

={(x,y)/3y+4x^2-4x+3=0

Dominio

y=(-4x^2+4x-3)/3

D: IR

Rango

4x^2-4x+3=-3y

4(x^2-x+1/4)+2=-3y

4(x-1/2)^2+2=-3y

(x-1/2)^2=(-2-3y)/4

x=√((-(2+3y))/4)+1/2

x=(√(-(2+3y))+1)/2

Luego se tiene:

-(2+3y)≥0

(2+3y)≤0

y≤-2/3 -2/3

Rango es: (-∞,-2/3)

f(x)=3x-2

g(x)=x^3

(f+g)(2)=2^3+3(2)-2=8+6-2=12

(f-g)(2)=3(2)-2-2^3=6-2-8= -4

(fg)(2)=(3(2)-2)(2^3 )=(6-2)(8)=32

(sec⁡x⁡〖+tan⁡〖x)(1-sin⁡〖x)=cos⁡x 〗 〗 〗

(1/cos⁡x +sin⁡x/cos⁡x )(1-sin⁡〖x)=cos⁡x 〗

((1+sin⁡x)(1-sin⁡x))/cos⁡x =cos⁡x

(1-sin^2⁡x)/cos⁡x =cos⁡x

cos^2⁡x/cos⁡x =cos⁡x

(tan⁡x+cos⁡x)/sin⁡x =sec⁡x+cot⁡x

tan⁡x/sin⁡x +cos⁡x/sin⁡x =sec⁡x+cot⁡x

(sin⁡x/cos⁡x )/(sin⁡x/1)+cot⁡x=sec⁡x+cot⁡x

sin⁡x/(sin⁡x cos⁡x )+cot⁡x=sec⁡x+cot⁡x

sec⁡x+cot⁡x=sec⁡x+cot⁡x

C

b 35° a

9°

A 81° c 64° B

21 pies

c/sin⁡C =b/sin⁡B

b=(c sin⁡B)/sin⁡C

b=((21pies) sin⁡〖64°〗)/sin⁡〖35°〗 =32,9 pies

La altura del poste es de 32,9 pies

0°≤x≤360°

csc^4⁡〖2x-4=0〗

1/sin^4⁡2x -4=0

sin^4⁡2x=4

sin⁡2x=∜(1/4)

x=sin^(-1)⁡0,707/2=22,5°

x=67,5°,112,5°,157,5°

5 sin⁡x tan⁡x-10 tan⁡x+3 sin⁡x-6=0

5 tan⁡x (sin⁡x-2)+3(sin⁡x-2)=0

(sin⁡x-2)(5 tan⁡x+3)=0

sin⁡x-2=0

〖x=sin〗^(-1)⁡(2)

x=∄

5 tan⁡〖x+3=0〗

x=tan^(-1)⁡((-3)/5)

x=-30,96°

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