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MATH 124 Calculus Test 1 - Limits, Integrals, and Series - Prof. Harold E. Donley, Exams of Mathematics

Dr. Ed donley's calculus for physics and chemistry test 1 from september 20, 2002. The test covers topics such as limits, integrals, and series. Students are required to find limits, evaluate integrals, determine convergence of series, and estimate sums.

Typology: Exams

Pre 2010

Uploaded on 08/19/2009

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MATH 124 Calculus for Physics and Chemistry
Test 1
Dr. Ed Donley
September 20, 2002 Name
1. (8 points) Find
0
)21(lim
/3
x
x
x
.
2. (16 points) Evaluate the following integrals, if they exist. If they don’t exist,
demonstrate why.
a)
2
1
3
ln xdxx
b)
9
0
9x
dx
pf3
pf4

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MATH 124 Calculus for Physics and Chemistry

Test 1

Dr. Ed Donley

September 20, 2002 Name

1. (8 points) Find 

   0 lim ( 1 2 )^3 / x x x

2. (16 points) Evaluate the following integrals, if they exist. If they don’t exist,

demonstrate why.

a) 

2 1

x^3 ln xdx

b) 

9 0 9 x dx

Page 2 of 4

3. (8 points) Determine whether or not

          (^11) 2 1 n n n

converges. If it does converge, find

its limit.

4. (32 points) Determine whether or not the following series converge. If possible, find

the limit.

a) ^

   0 3 2 i i

b) ^

    1 2 3 1 k k k

Name

Page 4 of 4

6. (5 points) Find a formula for the nth^ term of the sequence

7. (8 points) Find the 3rd^ and 37th^ terms of the sequence a 1 = 2, an = 0.23 an-1 + 1000.

8. (8 points) How many terms are needed to estimate 

n n n

with an error of at

most .0001?