Find a power series representation for the function. (Give your power series representation centered at x=0 .) f(x)=15+x

Step-by-step explanation:

Given

Required

The power series centered at

We have:

Factor out 5 from the denominator

Rewrite as:

Further, rewrite as:

Expand the bracket

Evaluate all exponents

Open brackets

Notice the pattern as:

So, the power series is:

third choice down

step-by-step explanation:

the first inequality is based on the number of adults and campers, and the second inequality is based on the cost of feeding both the adult and the camper.

we know that there is room for 525 people max.   it's ok to have less than 525, but it's not ok to have more than 525, so the inequality is less than or equal to.   the number combination of adults (x) and campers (y) cannot exceed this 525 max.   therefore:

x + y ≤ 525

now we talk about cost.   it costs $9 to feed one adult, so depending upon the number of adults you have (x) depends upon how much it will cost to feed that number of adults.   same with the campers, who cost $5 to feed.   the adults can be represented by 9x and the campers can be represented by 5y.   since the budget cannot exceed 1,200, the second inequality is:

9x + 5y ≤ 1200