Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 3
1. Determine the domain of the following functions in interval notation.
(a) f (x) = log2 (26x − 13)
(b) g(x) = ln (x − 9)
2. Below is the graph of f (t). Use it to find the given quantities.
5
4
3
2
1
0
-1
-2
-3
-3
(a) lim+ f (t)
t→−1
(b) lim+ f (t)
t→1
(c) lim− f (t)
t→1
(d) lim f (t)
t→1
-2
-1
0
1
2
3
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
3. Simplify the following expressions:
(a) 8log8 9
(b) log2 (42 )
(c) 3log9 4
(d) 64 log6 3
4. (a) Evaluate f (x) =
x
f (x)
0.9
0.99
0.999
1
DNE
1.001
1.01
1.1
ln x
x−1
at the given numbers correct to 4 decimal places.
(b) Guess the value of lim f (x).
x→1
Week 3
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
5. Use the change of base formula to evaluate log2.2 8.3 to 4 decimal places.
6. Determine the following limits, if they exist.
(a) lim 2x(x − 12)
x→10
(b) lim
x→−5
(c) lim
x→4
√
−16 − 5x
x2 +x−20
x−4
x2 −x+12
x−3
x→3
(d) lim
(2+h)2 −4
h
h→0
(e) lim
Week 3
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
7. Solve the following equations for x.
(a) 6 ln(x) = 1
(b) 2x+9 − 5 = 0
(c) log(7 − 7x) = 2
(d) 3(10)8x = 18
Week 3
Mr. Orchard’s Math 142 WIR
8. If f (x) =
Sections 1.5, 3.1
Week 3
x
+6
x ≤ 20
5
√
, determine the following limits.
101 − x x > 20
(a) lim− f (x)
x→20
(b) lim+ f (x)
x→20
(c) lim f (x)
x→20
9. Use the properties of logarithms to rewrite log8
of simpler logarithms.
z+7
x(y−2)2
as the sum and/or difference
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 3
10. For each part, determine the values of x for which g(x) is discontinuous.
(a) g(x) =
x+3
(x+3)(x+6)
(b) g(x) =
2xx −11x
x3 −12x2 +35x

x≤4
 5 − 2x
x−7 4<x<8
(c) g(x) =
 2
x −2
x≥8
11. Alice has invested money in an account which pays annual interest at 3.9% compounded
quarterly.
(a) How long will it take for the account to double in value? (Round to one decimal
place.)
(b) How long will it take for the account to triple in value? (Round to one decimal
place.)
Mr. Orchard’s Math 142 WIR
Sections 1.5, 3.1
Week 3
12. Find the value(s) of A that make f continuous everywhere, where
x2 −4
x<2
x−2
f (x) =
2
Ax − 2x − 6 x ≥ 2
13. The effective rate for a continuously compounded account is 5.6%. What is the nominal
rate for the account?