Calculus I |
Test #1
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September 26, 2001
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Name____________________ |
R. Hammack
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Score _______
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(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) = = = = =