7
f(x)=2^(3x)
f(1)=2³=8
f`(x)=3*2^(3x)*ln2
f`(1)=3*8*ln2=24ln2
y=8+24ln2*(x-1)
8
f(x)=ln(5x)
f(1)=ln5
f`(x_=1/(5x)*5=1/x
f`(1)=1
y=ln5+1*(x-1)=x-1+ln5
9
f(x)=f(x0+Δx)≈f(x0)+f`(x0)*Δx
x=2,037=2+0,037⇒x0=2,Δx=0,037
f(2,037)≈f(2)+f`(2)*0,037
f(2)=√[(4-3)/(4+5)]=√(1/9)=1/3
f`(x)=1/2*√[(x²+5)/(x²-3)]*[2x(x²+5)-2x(x²-3)]/(x²+5)²=
=1/2*√[(x²+5)/(x²-3)]*2x(x²+5-x²+3)/(x²+5)²=√[(x²+5)/(x²-3)]*8x/(x²+5)²=
=8x/√[(x²-3)(x²+5)³]
f`(2)=16/√(1*9³)=16/27
f(2,037)≈1/3+16/27*0,037=(9+16*0,037)/27=(9+0,592)/27=9,592/27≈0,355