1. ## open ended problems

i got two open ended problems i need help on.

1) Given the region defined by $f(x)=x^{2}+1$, use the stated number of rectangles to estimate the area under the curve.
a)2
b)4
c)6
d)8
I know what the graph of the function looks like, but I dunno what I'm supposed to do next to "estimate the area". In fact, I don't understand the question at all.

2) This is a big one.
A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

a) Draw diagrams illustrating the situation, some with shallow, wide pens, and some with deep, narrow pens. Find the total area of these pens.

b) Draw a diagram illustrating the general situation.

c) Write an expression for the total area.

d) Use the given info to write an equation relating the variables.

e) Write the total area as a function in terms of 1 variable.

f) Find the max value of the function and compare with your answer to (a).

If you could help me step by step here, I'd be real grateful. Thanks.

2. Originally Posted by DarthBlood
i got two open ended problems i need help on.

1) Given the region defined by $f(x)=x^{2}+1$, use the stated number of rectangles to estimate the area under the curve.
a)2
b)4
c)6
d)8
I know what the graph of the function looks like, but I dunno what I'm supposed to do next to "estimate the area". In fact, I don't understand the question at all.

2) This is a big one.
A farmer with 750 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle.

a) Draw diagrams illustrating the situation, some with shallow, wide pens, and some with deep, narrow pens. Find the total area of these pens.

b) Draw a diagram illustrating the general situation.

c) Write an expression for the total area.

d) Use the given info to write an equation relating the variables.

e) Write the total area as a function in terms of 1 variable.

f) Find the max value of the function and compare with your answer to (a).

If you could help me step by step here, I'd be real grateful. Thanks.
for #1 , research Riemann Sums.

for #2 see attached diagram ...

A = xy

P = 2x + 5y

work from there.