Calculus I – Test 1 – Review Problems MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Calculus I – Test 1 – Review Problems
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
1) If f(x) = x + 5 and g(x) = 8x – 9, find f(g(x)).
A) 2 2x – 1 B) 8 x + 5 – 9 C) 8 x – 4 D) 2 2x + 1
1)
2) If f(x) = x, g(x) =
x
4
, and h(x) = 4x+ 8, find h(g(f(x))).
A) x + 2 B) 4 x + 8 C) x + 8 D) x + 2
2)
Express the given function as a composite of functions f and g such that y = f(g(x)).
3) y =
2
6x + 9
A) f(x) = 6x + 9, g(x) = 2 B) f(x) = 2, g(x) = 6 + 9
C) f(x) =
2
x
, g(x) = 6x + 9 D) f(x) =
2
x
, g(x) = 6x + 9
3)
Use the laws of exponents to simplify. Do not use negative exponents in your answer.
4) (7-7)
-6
A) 7
13 B) 1
7
42 C) 7
42 D) 1
7
13
4)
Solve the problem.
5) The amount of particulate matter left in solution during a filtering process decreases by the
equation P = 1000(2)-0.8n, where n is the number of filtering steps. Find the amounts left for n = 0
and n = 5. (Round to the nearest whole number.)
A) 1000, 16,000 B) 2000, 63 C) 1000, 31 D) 1000, 63
5)
Find the inverse of the function.
6) f(x) =
4
x – 9
A) f-1(x) =
-9 + 4x
x
B) f-1(x) =
9x + 4
x
C) f-1(x) =
x
-9 + 4x
D) Not a one-to-one function
6)
Find the exact function value.
7) sec-1( 2)
A) 7π
4
B) 3π
4
C) π
4
± 2πn, 7π
4
± 2πn D) π
4
7)
1
Graph the function.
8) y = (-4x)2/3 + 2
-10 -8 -6 -4 -2 2 4 6 8 x
10 y
8
6
4
2
-2
-4
-6
-8
-10
-10 -8 -6 -4 -2 2 4 6 8 x
10 y
8
6
4
2
-2
-4
-6
-8
-10
A)
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
B)
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
C)
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
D)
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
-5 -4 -3 -2 -1 1 2 3 4 5 x
y
5
4
3
2
1
-1
-2
-3
-4
-5
8)
Find the average rate of change of the function over the given interval.
9) y =
3
x – 2 , [4, 7]
A) –
3
10 B) 7 C) 2 D) 1
3
9)
2
Use the graph to evaluate the limit.
10) lim
x→0
f(x)
-4 -3 -2 -1 1 2 3 4 x
y
4
3
2
1
-1
-2
-3
-4
-4 -3 -2 -1 1 2 3 4 x
y
4
3
2
1
-1
-2
-3
-4
A) -1 B) 0 C) does not exist D) 1
10)
Provide an appropriate response.
11) Let lim
x → 5
f(x) = 6 and lim
x → 5
g(x) = 10. Find lim
x → 5
f(x)
g(x) .
A) 5
3
B) 5 C) 3
5
D) -4
11)
Find the limit, if it exists.
12) lim
x → 6
6 – x
6 – x
A) 1 B) Does not exist C) -1 D) 0
12)
13) lim
x → 3
x
2 + 7x – 30
x – 3
A) 7 B) 13 C) Does not exist D) 0
13)
Provide an appropriate response.
14) It can be shown that the inequalities -x ≤ x cos
1
x
≤ x hold for all values of x ≥ 0.
Find lim
x→0
x cos
1
x
if it exists.
A) 0.0007 B) 0 C) 1 D) does not exist
14)
A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number ε is given. Find a number δ > 0 such
that for all x, 0 < x – c < δ ⇒ f(x) – L < ε.
15) f(x) = -5x – 6, L = -21, c = 3, and ε = 0.01
A) δ = 0.002 B) δ = 0.001 C) δ = -0.003333 D) δ = 0.004
15)
3
Determine the limit.
16) lim
x → 7-
f(x), where f(x) =
-3x – 4 for x < 7
5x – 3 for x ≥ 7
A) 32 B) -3 C) -2 D) -25
16)
Find the limit using lim
x=0
sinx
x
= 1.
17) lim
x→0
sin 5x
sin 4x
A) 0 B) 5
4
C) 4
5
D) does not exist
17)
Find all points where the function is discontinuous.
18)
A) None B) x = -2 C) x = -2, x = 2 D) x = 2
18)
Find the limit and determine if the function is continuous at the point being approached.
19) lim
x→7
sec(x sec2x – x tan2x – 1)
A) sec 6; no B) csc 6; yes
C) sec 6; yes D) does not exist; no
19)
Find the limit.
20) lim
x→∞
x2 + 5x + 15
x3 + 4×2 + 19
A) ∞ B) 0 C) 15
19 D) 1
20)
21) lim
x → -8-
1
x + 8
A) ∞ B) -1 C) -∞ D) 0
21)
Divide numerator and denominator by the highest power of x in the denominator to find the limit.
22) lim
t→∞
9t2 – 27
t – 3
A) 27 B) does not exist C) 9 D) 3
22)
4
Answer Key
Testname:
1)
A
2)
C
3)
C
4)
C
5)
D
6)
B
7)
D
8)
C
9)
A
10)
C
11)
C
12)
B
13)
B
14)
B
15)
A
16)
D
17)
B
18)
C
19)
C
20)
B
21)
C
22)
D
5