MATH 141 Midterm: MATH141 South Carolina 141 f 05 f
Math 141, Final Exam, Fall 2005
Write your answers as legibly as you can on the blank sheets of paper provided.
Use only one side of each sheet. Be sure to number your pages. Put your solution
to problem 1 first, and then your solution to number 2, etc.; although, by using
enough paper, you can do the problems in any order that suits you.
There are 23 problems. Problems 1 through 7 are worth 8 points each. Each of the
other problems is worth 9 points. The exam is worth 200 points. SHOW your work.
Make your work be coherent and clear. Write in complete sentences whenever this
is possible. CIRCLE your answer. CHECK your answer whenever possible.
No Calculators.
If I know your e-mail address, I will e-mail your grade to you. If I don’t already
know your e-mail address and you want me to know it, then send me an e-mail.
Otherwise, get your grade from VIP.
You might find the following formulas to be useful:
n
X
k=1
k2=n(n+ 1)(2n+ 1)
6and
n
X
k=1
k3=n2(n+ 1)2
4.
I will post the solutions on my website a few hours after the exam is finished.
1. Let y= 2x. Find dy
dx .
2. Let y= cos(cos x) . Find dy
dx .
3. Let y=x2(arcsin x)3. Find dy
dx .
4. Let y= sin xZx
0
sin(t2)dt. Find dy
dx .
5. Find Z2
1
x2dx .
6. Find Zπ
9
π
12
sec23θdθ .
7. Find Z1
−1
x2dx
√x3+ 9 .
8. Find Z√π
2
0
5xcos(x2)dx .
Document Summary
Write your answers as legibly as you can on the blank sheets of paper provided. Put your solution to problem 1 rst, and then your solution to number 2, etc. ; although, by using enough paper, you can do the problems in any order that suits you. Problems 1 through 7 are worth 8 points each. Each of the other problems is worth 9 points. Write in complete sentences whenever this is possible. If i know your e-mail address, i will e-mail your grade to you. If i don"t already know your e-mail address and you want me to know it, then send me an e-mail. You might nd the following formulas to be useful: n. Xk=1 k2 = n(n + 1)(2n + 1) I will post the solutions on my website a few hours after the exam is nished: let y = 2x . Find dy dx : let y = cos(cos x) .
