HW 1: REVIEW & INTEGRATION

MA 124, SUMMER I

For all homework, BC&Gv2 will refer to the second edition of Calculus: Early Tran-scendentals by Briggs, Cochran, & Gillett. For problem numbers, I will write “bookch.section.number”, i.e. BC&Gv2 1.4.3 will refer to chapter 1, section 4, exercise 3 fromthe textbook and BC&Gv2 2.R.5 is referrering to chapter 2, review exercises, exercise 5from the textbook.

When you turn in the homework, please write on the top of the page how long it took youto complete, and how difficult it was on a scale of 1-5, i.e. “1.5 hrs. - 3”. This homeworkconsists of more problems than a typical homework as it should be review.

BC&Gv2 1.R.16) Composite Functions: Find functions f and g such that h = f ◦ g, i.e.h(x) = f(g(x)).

a) h(x) = sin(x2 + 1)b) h(x) = (x2 − 4)−3c) h(x) = ecos(2x)

BC&Gv2 1.R.24) Graphs of logarithmic and exponential functions: The figure shows thegraphs of y = 2x, y = 3−x, and y = − ln(x). Match each curve with the correct function:

BC&Gv2 2.R.12) Determine the following limit:1

2 MA 124, SUMMER I

limx→4

x3 − 7x2 + 12x4 − x

BC&Gv2 2.R.31) Limits at infinity:

limx→∞

2x− 34x+ 10

BC&Gv2 2.R.42) Find all vertical and horizontal asymptotes of the following functions:

f(x) =2x2 + 6

2x2 + 3x− 2BC&Gv2 3.R.15 (polynomial):

d

dx

(2

3x3 + πx2 + 7x+ 1

)BC&Gv2 3.R.19 (chain rule):

d

dθ

(4 tan

(θ2 + 3θ + 2

))BC&Gv2 3.R.21 (quotient rule):

d

du

(4u2 + u

8u+ 1

)BC&Gv2 3.R.28 (product rule):

d

dw

(e−w ln(w)

)BC&Gv2 4.R.6) Find the critical points of the following function on the given interval.Identify the absolute maximum and minimum values if they exist.

f(x) = sin(2x) + 3 on [−π, π]

BC&Gv2 4.R.21) Optimization: A right triangle has legs of length h and r, and a hy-potenuse of length 3. It is revolved about the leg of length h to sweep out a right circularcone. What values of h and r maximize the volume of the cone? The volume of a cone isgiven by V = πr

2h3 .

HW 1: REVIEW & INTEGRATION 3

BC&Gv2 4.R.73, 77) Find the following indefinite integrals:∫(1 + cos(3θ)) dθ∫

12

xdx