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Name: Perm number:

Test 2

Time: 50 minutes 1. Find the derivatives of the following functions:

(a) sin(3x)

(d) x2ex

(e) √

x sin(3x)

1

(2)

2. As of the census of 2000, there were 92,325 people, 35,605 households, and 18,941 families residing in the city of Santa Barbara. The per capita income for the city was $26,466. Assuming that the average income per capita is increasing at the rate of $1225 per year, and that the population is growing by roughly 630 new residents annually, what was the change in total income in Santa Barbara in 2000?

2

(3)

3. Find local minimas and local maximas of the function f (x) = 3x5− 5x3+ 3.

3

(4)

4. Find an approximate value of√ 9999.

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