means to say that for any given 
, we can find 
such that anytime 
(i.e. the whenever 
is "close enough" to 5), we can guarantee that 
(i.e. the value of 
is "close enough" to the limit value).
What we want to end up with is
Dividing both sides by 3 gives
which suggests 
is a sufficient threshold.
The proof itself is essentially the reverse of this analysis: Let be given. Then if
and so the limit is 7. QED
F(t) = P.e^(r.t) [ and not as you wrote it f(t)+Pe^rt]
plug in:
f(t) = 8.e^(0.08t) (where e = 2.718 and t=8 given, f(8))
f(8) = 8.(2.718)^(0.08*8) = 21.74^(0.64)
f(8) = 7.17
Answer:
(3 V/ 4 pi) ^(1/3) = r
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
We want to solve for r
Multiply each side by 3/4
3/4 V = 4/3*3/4 pi r^3
3/4 V = pi r^3
Divide each side by pi
3/4 V/ pi = pi/pi r^3
3 V/ 4 pi = r^3
Take the cube root of each side
(3 V/ 4 pi) ^(1/3) = ( r^3) ^1/3
(3 V/ 4 pi) ^(1/3) = r
It would be: -2/3 * -9/10 = 18/30 = 3/5
So, option B is your answer.
Hope this helps!
