Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
1. Determine the domain of the following functions in interval notation.
(a) g(x) = ln(13 − 10x)
(b) f (x) = log7 (10x )
(c) h(x) = log
q
1
x2 −2
2. Use the change of base formula to evaluate each logarithm to 4 decimal places.
(a) log13 7
(b) log8 67.4
(c) log3 8.1
Week 2
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 2
3. Solve the following equations for x:
(a) log x =
−5
3
x
(b) 2log4 4 = 4
(c) ln(log 8x) = 0
(d) ln x2 − ln x4 = 1
4. Fred Jones is saving up to buy a van (named the Mystery Machine). He has three
fourths of the money now, which he puts into a bank account compounded quarterly at
an annual rate of 6.2%. How long will it take him to get the money for his van?
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
5. Write the following expressions with only one logarithm.
(a) log7 z − log7 x
(b) 2 ln x + ln y
(c)
1
3
ln z − 4 ln z 2 + ln x +
ln y
2
6. Expand the following expressions in terms of log x, log y, and log z.
3
(a) log xz y
(b) log
q
3
x2 y −5
x3 z
Week 2
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 2
7. The graph of g(x) is given below.
12
10
8
6
4
2
0
-2
-4
-6
-2
-1
0
1
(a) Find lim− g(x). (If it does not exist, write DNE.)
x→0
(b) Find lim+ g(x). (If it does not exist, write DNE.)
x→0
(c) Find g(0).
(d) Find lim g(x). (If it does not exist, write DNE.)
x→0
2
3
4
5
Mr. Orchard’s Math 142 WIR
8. Let f (x) =
sin x
.
x
x
0.1
0.01
0.001
(a)
0
−0.001
−0.01
−0.1
(b) Guess lim
x→0
Fill in the following table to 7 decimal places:
f (x)
Does Not Exist
sin x
.
x
9. Simplify the following
(a) log3 3−2
(b) 5log5 13
(c) 2log2 (log3 9)
Sections 1.5, 3.1
Week 2
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
10. Find the following limits (if it does not exist, write DNE):
(a) lim 3x3 + 4x2 + 5x + 6
x→1
x2 +x−12
x−3
x→3
(b) lim
x2 +x−6
x→2 x−2
(c) lim
(1+h)2 −1
h
h→0
(d) lim
|x|
x→0 x
(e) lim
(f) Let f (x) =
2
.
3x−7
Find lim
h→0
f (3+h)−f (3)
.
h
Week 2
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 2
11. Find the value of A that completes the equation: lim x2 + Ax − 22 = −10.
x→2
12. f (x) =
10 − x2 x ≤ 3
Find the following (if it does not exist, write DNE).
x−2
x>3
(a) lim+ f (x).
x→3
(b) lim− f (x).
x→3
(c) lim f (x).
x→3
(d) f (3).
(e) Is f continuous at x = 3? Justify your answer.
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
13. Determine the x values where h is discontinuous. h(x) =
Week 2

 4 − 2x

x2 −1
x−1
√
6
x2
x≤1
1<x<6
−9
x≥6
14. In a bank account with continuously compounded interest at an annual rate of 4.5%,
how long will it take for $3000 to grow to $3700?
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 2
 2
 x + 6c − 5 x < 2
27
x=2
15. Let g(x) =

2c − x + 9 x > 2
(a) Find lim− g(x) in terms of c. (If it does not exist, write DNE.)
x→2
(b) Find lim+ g(x) in terms of c. (If it does not exist, write DNE.)
x→2
(c) For what values of c does lim g(x) exist?
x→2
(d) For the above value of c, what is lim g(x)?
x→2
(e) For the above value of c, is g(x) continuous at x = 2? Mathematically justify your
answer.