HW #1 Mat 141
Shark
Attach your work to this sheet.
Name__________________________________
(1) Solve the trigonometric equation: sin(2 x  1) 

(a) x  6

(b) x  6

(c) x  3

(d) x  3
3
2
1
2
1
2
1
2
1
2
(2) Differentiate the function, and simplify: f ( x)  sin(arccos( x ))
(a) f ( x)  arcsin( x)
x
(b) f ( x) 
1  x2
(c) f '(x) = cos(arcsin(x))
x
(d) f ( x) 
1  x2
(3) Evaluate the integral:
1
x
arctan    C
5
5
(b) arctan(5 x)  C
(c) 5arctan( x)  C
x
(d) arctan    C
5
(a)
dx
 25  x
2
(4) Evaluate the integral by completing the square in the denominator:
(a)
1
 ( x  3) 
arctan 
 +C
2
 2 
(b)
1
 ( x  3) 
arctan 
C
4
2 

(c)
1
 ( x  3) 
arctan 
C
2
2 

x
2
dx
 6 x  11
 ( x  3) 
(d) arctan 
C
2 

(5) Dark City had a population of 350,000 in 1990, and has increased exponentially since
then, to 475,000 in 2008. Project the population in 2015.
Approximately:
(a) 523,611
(b) 534,955
(c) 622,311
(d) 582,417
(6) If 8 grams of Carbon is present in a fossil, how long will it take until there are only 3
grams left? (fact: the half-life of carbon is 5715 years)
Approximately:
(a) 7912 years.
(b) 8086 years.
(c) 12,437 years.
(d) 10, 372 years.