Chapter 5 Final Exam Problems:

1) Consider the table of values of the function f:

Table 1

t / 1 / 3 / 5 / 7 / 9 / 11 / 13
f(t) / 4 / 2 / 1 / -2 / -6 / -4 / -1

Let LHS = f (t0) t + f (t1) t + f(t2) t+...+f(tn-1)t denote the left hand Riemann sum and

RHS= f (t1) t + f (t2) t + f(t3) t+...+f(tn)t denote the right hand Riemann sum.

(a)  Using Table 1, fill in the values needed to compute LHS and RHS in the table below, then compute LHS and RHS:

Table 2

t / n / t0 / t1 / t2 / t3 / f (t0) / f (t1) / f (t2) / f (t3)
3 / 1 / 9

(b)  Using Table 1, fill in the values needed to compute LHS in the table below, then compute LHS:

Table 3

t / n / t0 / t1 / t2 / t3 / f (t0) / f (t1) / f (t2) / f (t3)
4 / 2 / 11

(c)  Using Table 1, fill in the values needed to compute the midpoint approximation in the table below, then compute the midpoint approximation:

Table 3

t / n / t0 / t1 / t2 / t3 / f (t0) / f (t1) / f (t2) / f (t3)
4 / 1 / 5 / -6

2) A woman drives 10 miles, accelerating uniformly from rest to 60 mph. Graph her velocity versus time. How long does it take her to reach 30 mph?

3) The graph of the first derivative f’ of a function f is shown below. (Insert graph here, same one as last year’s final)

Fill in the table of values for f(x) given that f(6)=55:

x / 0 / 2 / 6 / 10 / 14 / 18
55