Answer:
(7)
error percentage is 0.6%
(8)
Graph-C
Step-by-step explanation:
(7)
we are given cube
Let's assume edge of cube =x
so, volume of cube will be
[tex]V(x)=x^3[/tex]
we are given
V=125000
so, we can find 'x'
[tex]125000=x^3[/tex]
[tex]x=50[/tex]
So,
[tex]a=50[/tex]
now, we can use linear approximation formula
[tex]L(x)=V(a)+(x-a)V'(a)[/tex]
[tex]L(x)=V(a)+(\Delta x)V'(a)[/tex]
we have
[tex]\Delta x=0.1[/tex]
we can plug a=50
[tex]L(x)=V(50)+(0.1)V'(50)[/tex]
[tex]V(x)=x^3[/tex]
we can find derivative
[tex]V'(x)=3x^2[/tex]
now, we can plug x=50
[tex]V'(50)=3(50)^2[/tex]
[tex]V'(50)=7500[/tex]
now, we can plug these values
and we get
[tex]L(x)=V(50)+(0.1)\times 7500[/tex]
[tex]L(x)=V(50)+750[/tex]
[tex]L(x)-V(50)=750[/tex]
so, error is
[tex]error=750[/tex]
now, we can find percentage error
Percentage is
[tex]=\frac{750}{125000}\times 100[/tex]
=0.6%
so, error percentage is 0.6%
(8)
we are given
[tex]s(t)=2e^{-1.5t}sin(2\pi t)[/tex]
We will find derivative
To get velocity , we will find derivative
[tex]s'(t)=\frac{d}{dt}\left(2e^{-1.5t}\sin \left(2\pi t\right)\right)[/tex]
we can use product rule
and we get
[tex]s'(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]
so, we get velocity equation as
[tex]v(t)=-3e^{-1.5t}sin(2\pi t)+4\pi e^{-1.5t} sin(2\pi t)[/tex]
now, we can draw graph
we can see that firstly , we get maxima and then minima
so, our graph would be
graph-C........Answer
