Calculus I Test #1 September 26, 2001 Name____________________ R.  Hammack Score _______

(1)
(a)   sin 30π = 0

(b)    cos =
(c)   Find all values of  θ  for which  cos θ =

+ 2nπ    and    - + 2nπ   where n is an integer.

(2) In this problem   0 < x < and   sin x =

(a)    cos x  = (use the identity x = 1 to solve for cos x.)

(b)    tan x = = (here we used the fact   tan x = )

(3) In this problem  f(x) =   and   g(x) = x - 4.

(a)    ()(x)  = =

(b)   (f º g)(x) = = =

(c)   (g º g)(x) = g(x) - 4 = x - 4 - 4 = x - 8

(4) This problem concerns the function  f(x) =

(a)    f(x + 2) =

(b)    Find the domain of f.  Be sure to show your work.

We require that ≥ 0 and x is not 0.
i.e. we require  ≥ 0 and x ≠ 0.

Thus the domain is [-2, 0) [2, ∞)

(c)   Write f as a composition of two functions.
Let h(x) =
and g(x) =
Then f(x) = h(g(x))

(d)     f(x) =  = = =

(e)    f(x) =  =  = =
= = 0

(f)     f(x) =    = ∞  (numerator gets close to -4, denominator is close to 0, negative)

(5) Calculate the limits.

(a)    (3- 4x + π) = 3- 4(3) + π = 15 + π

(b)     =  = = 0

(c)      =  =

(d)    = ∞  (note, top approaches 18 while bottom is positive, approaching 0)

(e)    =  =  = =  = = 1

(f)    =  = =  = =