MATH 123
Review Questions for Exam 1
1. Use Riemann summation with the right endpoint evaluation and four
intervals to approximate the integral R2
0x3dx.
2. Use Simpson’s Rule approximation for the definite integral R2
0x3dx using
4 subintervals.
(Recall Simpson’s Rule: Rb
af(x)dx ≈b−a
3n[y0+ 4y1+ 2y2+· · · +y2n] ).
3. Solve the initial value problem.
a. dy
dx =y2,y(0) = 2.
b. d2y
dx2+ 2dy
dy −3 = 0, y(0) = 1, y0(0) = 0.
4. Suppose that a radioactive substance decays with a half life of 70 days,
and 60 grams are initially present.
a. Find a formula for the amount of the substance present at time t.
b. How long will it be before there are 20 grams present?
5. Suppose that an initial population of 25000 bacteria grows exponentially
at the rate of 2 percent per hour. Find the number y(t) of bacteria at time t.
How long does it take for the population to double?
For 6 - 9, (a) determine if the sequence is strictly increasing, strictly decreasing,
or neither, and (b) determine if the sequence converges and, if so, to what limit.
6. sn= 5 −2
n.
7. sn=2n
n+1 .
8. sn=n
en.
9. sn=2+sn−1
3
1