1/1*2 +1/2*3 +....+1/19*20=1-1/1*2+1/1*2-1/2*3 +......+1/18*19-1/19*20=
=1-1/19*20=379/380
1/1*2=1- 1/1*2
1/2*3=1/1*2-1/2*3
...........................
1/19*20=1/18*19 -1/19*20
Производная = -6х + 9
ищем критические точки:
-6 х + 9 = 0
6 х = 9
х = 9/6= 3/2 = 1,5
-3х² + 9х + с = -5
-3·2,25 + 9· 1,5 + с = -5
-6,75 + 13,5 + с = -5
с = - 5 + 6,75 - 13,5
с = -11,75
№ 4
f(x) = 1/x + x² ; g(x) = 2/x - 8
a) f(-1) = -1 +1 = 0
g(-1) = -2 -8 = -10
g(3) = 2/3 - 8 = -22/3
0 -10 -22/3 = -10 - 7 1/3 = -17 1/3
б) f(0,5) = 2 + 0,25 = 2,25
g(2) = 1 - 8 = -7
f(0,5) - 3g(2) = 2,25 -3*(-7) = 23,25
в) f(-2) = -1/2 + 4 = 3,5
g(0,5) = 1 - 8 = -7
4f(-2) - g(0,5) = 4*3,5 +7 = 14 +7 = 21
г) f(1/4) = 4 + 1/16 = 4 1/16
g(-2/5) = -5 - 8 = -13
16f(1/4) + 2g(-2/5) = 16*65/16 + 2*(-13) = 65 -26 = 39
№5
f(x) = x² + 5x -1
a) x² + 5x -1= -1
х² +5х = 0
х = 0 и -5
б)x² + 5x -1 = 5
х² + 5х -6=0
х = -6 и 1
в)x² + 5x -1 = -5
х² + 5х +4 = 0
х = -4 и -1
г)x² + 5x -1 = -6,25
х² + 5х + 5,25= 0
х = -7/2 и --3/2