ECON 11A Study Guide - Midterm Guide: Precalculus
ams 11aStudy Guide 1 econ 11a
Precalculus and Limits
1. A certificate of deposit offers an interest rate of 5.5% compounded daily for a term of 4
years. How much would you have to invest initially to have $25000 when the CD matures?
2. Use the change of base formula to compute the following logarithms. Do not use a
calculator — express your answers in terms of ln 2,ln 3,ln 5,and ln 7. For example
log7100 = ln 100
ln 7 =ln 102
ln 7 =2 ln 10
ln 7 =2(ln 2 + ln 5)
ln 7 =2 ln 2 + 2 ln 5
ln 7 .
(a) log536 =
(b) log20 21 =
(c) log10 √75 =
(d) log21
1
3
√50
3. Simplify the following expressions using properties of the natural log function.
(a) ln x2+ 3x+ 1
5x+ 3 =(b) ln 3
s5xy3
x2+y2=
4. Solve the equations.
(a) 3x2+ 5x−8 = 0 (b) 2x+ 1
x−2=3x+ 5
8−2x
5. Solve the pairs of equations.
(a) 4x+ 5y= 7
3x+ 4y= 13 (b) 3x−2y= 1
5x+y= 2 (c) x2+ 2x−3y=−1
4x+ 2y= 14
6. Compute the following limits.
(a) lim
x→3
x3−8
x−2=
(b) lim
x→2
x3−8
x−2=
(c) lim
x→∞
x3−8
x−2=
(d) lim
h→0
(x+h)2−x2
h=
(express your answer in terms of x).
(e) lim
y→∞
5y4+ 300y2−60y+ 1000
20000 −3y+ 4y3−0.01y4=
(f) lim
x→0
√4 + x−2
x=
(g) lim
t→2+
t−2
√t−2=
(h) lim
x→0−
x
|x|=
(i) lim
x→0+
x
|x|=
Note: The last 3 limits are one-sided limits.
Document Summary
Precalculus and limits: a certi cate of deposit o ers an interest rate of 5. 5% compounded daily for a term of 4 years. How much would you have to invest initially to have when the cd matures: use the change of base formula to compute the following logarithms. Do not use a calculator express your answers in terms of ln 2, ln 3, ln 5, and ln 7. For example log7 100 = ln 100 ln 7 ln 102 ln 7. 2 ln 2 + 2 ln 5 ln 7 ln 7 (c) log10 (d) log21. 5xy3 x2 + y2 = (a) log5 36 = (b) log20 21 = (cid:18) x2 + 3x + 1 (cid:19) 5x + 3 (a) ln: simplify the following expressions using properties of the natural log function, solve the equations. (a) 3x2 + 5x 8 = 0, solve the pairs of equations. (cid:26) 4x + 5y = 7.
