156
2
f(x)=x-1
h→0
f(x+h)-f(x)=lim[(x+h)-1-(x-1)]/h=lim(x+h-1-x+1)/h=limh/h=1
4
f(x)=x²+2
h→0
lim[(x+h)²+2-(x²+2)]/h=lim(x²+2xh+h²+2-x²-2)/h=lim(2xh+h²)/h=
=lim(2x+h)=2x+0=2x
6
f(x)=2x³+x
h→0
lim[(x+h)³=(x+h)-(2x³+x)]/h=lim(2x³+6x²h+6xh²+h³-2x²-x)/h=
=lim(6x²h+6xh²+h³+h)/h=lim(6x²+6xh+h²+1)=6x²+6x*0+0+1=6x²+1
158
2
f(x)=-4x
f`(x)=-4
4
f(x)=-7x-8
f`(x)=-7
1
s(t)=0,3t-1,t1=2,t2=8
vср=Δs/Δt=[s(t2)-s(t1)]/(t2-t1)=(0,3*8-1-0,3*2+1)/(8-2)=(2,4-0,6)/6=1,8/6=0,3
v(t)=s`(t)=0,3
v(2)=0,3
v(8)=0,3
2
f(x)=5x-6
h→0
f`(x)=lim[5(x+h)-6-(5x-6)]/h=lim(5x+5h-6-5x+6)/h=lim(5h)/h=lim5=5