For some reason, I'm not getting this....

The volume of an object is given by $\displaystyle V=[pi(4.5(t)+1)^2(t)]$ If t changes from 4 to 5:

Find dV and delta(V)

Heres how I am solving it:

Vprime= pi(4.5t+1)^2 +pi*t(2)(4.5t+1)(4.5)

dV= [Vprime(t)]*[dt].. dt=1 and t=4 so:

[pi(4.5(4)+1)^2 +pi*(4)(2)(4.5(4)+1)(4.5)][1]= 3282.96

deltaV=f(t+delta(t))-f(t) so:

deltaV=f(4+1)-f(4)=

[pi(4.5(5)+1)^2(5)]-[pi(4.5(4)+1)^2(4)]=4138.26

dV approximates delta(V) so the numbers should be very close but as you can see, they're not.

Can anyone help?