Help needed with calculus questions

**calculus-geeks09** · December 18th 2008, 04:39 PM

determine the derivative of F(x)=(cos(2x-4))^3 at x=pie/b
determine d/dx 3x^4-3x/3x^4+3x
compute 4x^2x^3+4dx
an open rectangular box with volume 6m^3 has a square base. Express the surface area of the box as a function s(x) of the length x of a side of the base .
a box with an open top is to be constructed from a rectangular peice of cardboard with dmensions. b=5in. a=28in by cutting out equal squares of side x at each corner and then folding up the sides. find the maximum volume.
a spherical balloon with raduis r inches has volume 4/3pie^3. Find a function that represents the amount of air required to inflate the balloon from a radius of r innches to a radius of r+1 inches.
Lim as t approaches 2= t^2-4/t^3-8
absolute max. y=36-x (-6,6)
How many points of inflection in this graph

f(x)=12x^3=14x^2-7x-p

10. estimate the area from 0 to 5 under the graph
f(x)=81-x^2 using 5 rectangles from right end points.

**anywho** · December 18th 2008, 05:05 PM

Would you type those up using LaTex? There is a subsection with a tutorial. I will help more if you can do that since I don't want to type them up and make sure that we are on the same page. I will tell you that for number nine find y'' and set it to zero and solve to find the inflection points.

Edit:I typed this up yesterday and it should help you find 10's answer just change the interval, $\Delta x$ , the summation, and where it says left use right
a) Sketch the region R.
Simply sketch f(x) on the given interval

b) Partition [0,2] into 4 subintervals and show the four rectangles that LRAM uses to approximate the area of R. Compute the LRAM sum without a calculator.
First you need to find the width of the 'subintervals'. We will call the width $\Delta x$ . To find $\Delta x$ on the interval $[a,b]$ we use the following equation $(b-a)/n$ where $n$ is the number of subintervals.

You are doing an LRAM so you use the left point when making your rectangles. To find the height just insert the $x$ into $f(x)$ where you need to find the height.

The area under curve (what you are finding) is - $Area= A_1 + A_2 ... + A_n$ . To simplify this we can do a summation - $\sum_{j=0}^{2} A_j = \Delta x \sum_{j=0}^{2} f(x_j)$

Let me know if that makes any sense.