1) a) 4+12x+9x2
4+12x+18
22+12x
2(11+6x)
б) 25-40х+16х2
25-40х+32
57-40х
г) -56а+49а*2+16
-56а+98а+16
42а+16
2(21а+8)
2) a) (y-1)(y+1) б) p^2-9 г) (3x-2)(3x+2) д) (3x)^2-2^2 е) a^2-3^2
y^2-1 (3x)^2-2^2 9x^2-4 a^2-9
в) 4^2-(5y^2) 9x^2-4
16-25y^2
4) a) a3-b3 б) 27a3+8b3
3(a-b) 81a+24b
3(27a+8b)
1) f(x)=x2- 4; x0= 4
f`(x) = 2x
f`(4) = 2*4 = 8
2) f(x)=x sinx; x0= π/2
f`(x) = sinx + xcosx
f`(π/2) = sin(π/2) + (π/2)cos(π/2) = 1 + (π/2)*0 = 1
3) f(x)=sin2x; x0= π/2
f`(x) = 2cos2x
f`(π/2) = 2*cos[2*(π/2)] = 2cosπ = - 2
4) f(x)= 2x+cos2x; x0 = π/12
f`(x) = 2 - 2sin2x
f`(π/12) = 2 - 2sin[2*(π/12)] = 2 - 2sin(π/6) = 2 - 2*(1/2) = 2 - 1 = 1