1. Consider the differential
equation
Use EulerÕs method with 
to approximate y(2).
2. Consider the definite
integral
a. Use the midpoint rule with
n=2 subintervals to approximate this integral with a Riemann sum.
b. Define a Òleft point ruleÓ
for Riemann sums to be an approximation to the area under the curve using areas
of rectangles whose heights are taken to be the value of the integrand at the
left endpoint of each subinterval. Use the left point rule with n=2 rectangles
to approximate this integral as a Riemann sum.
c. Sketch a graph of 
for 
showing the
rectangles used for the midpoint rule and the rectangles used for the left
point rule.
3. Describe the relationship
between (A) solving the differential equation
using EulerÕs method with a
given value of h to approximate 
and (B)
approximating the integral
using a left point rule with
n subintervals. How should h and n
be related to give the same approximation?