If you're just integrating a vector-valued function, you just integrate each component:


The first integral is trivial since
.
The second can be done by substituting
:

The third can be found by integrating by parts:



82.75 minus the cost of the mug
Which equals 75 dollars and 75 divided by the cost of the refills which is 3.25 equals 24 refills
Answer:
16 days
Step-by-step explanation:
Given that:
Number of paramecium Aurelia doubles every 1.25days
5 days ago ; number of paramecium Aurelia = 1
How many are there now?
Using the relation :
Multiplier^(total number of days / time it takes to multiply)
Multiplier = doubles = 2
Total number rof days =. 5
Time it takes to. Multiply = 1.25
The formula becomes :
Number(n) of ptotozoan in 5days is given by 2^(5/1.25)
n = 2^(5/1.25)
n = 2^4
n = 2 * 2 * 2 * 2 =. 16
The asymptote for f(x) is y = 0
Notice the asymptote for g(x) is y = -1, which shift f(x) down 1
apply this to f(x)'s rule: 
Notice the graph of f(x) is shifted right 2 units...this horizontal movement must be applied to the x in f(x)'s rule: 