Homework 2
Due February 19, 2014
(1) Find a solution to the dierential equation
dy
1
= (x2 1) that satises y(0) = 2.
dx
2
(2) Use implicit dierentiation to nd the equation of the tangent line to the curve y 2 (y 2
4) = x2 (x2 5) at the point (0, 2). (Thi
1. Position, Velocity, Acceleration
(1) A particle moves in a straight line and has acceleration given by a(t) = 6t + 4. Its initial
velocity is v(0) = 6 cm/s and its initial displacement is s(0) = 9 cm. Find its position
function s(t).
(2) A ball is thro
Final Review
1
Areas and Distances
1. Write the following expressions as a denite integral:
n
(a) lim
n
tan(3 +
i=1
n
(b) lim
n
(
i=1
n
5i
5
1)3 + 1)
n
n
4i
2(2+ n )
(c) lim
n
2i 2
)
n n
i=1
4
n
2. For each of the integrals and values of n below, do the
HOur Exam #1
Math 3
February 4, 2014
Name (Print):
Last First
On this, the rst of the two Math 3 hourlong exams in Winter 2014, and on the second hourulong
exam, and on the nal exam, I will work individually, neither giving nor receiving help, guided by
I. Mari i bmm
2
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Eaters Meme
February 8, 2014
Draw part of the slope field for the differential equation 3: : y 3r: 1. Extra Practice
(1) Perform the following approximations (by hand):
(a) If g; : m + 2y and 3(0) 3 1, approximate y(2) using As: a: 1/2.
(b) If % = my and
WNW NWng
- February 8, 2014
Draw part of the slope field for the differential equation % : y m a: 1. Extra Practice
(1) Perform the following approximations (by hand):
(a) If j: = 3: + 2y and 3(0) 2 1, approximate y(2) using A3: = 1/2.
p lik.r iximm
Relate Rates
(1) A water tank has the shape of an inverted circular cone with base radius 2 m and height
4m. If water is being pumped into the tank at a rate of 2 m3 /min, nd the rate at which
the water level is rising when the water is 3 m deep.
(2) A bo
Math 3, Winter 2014 Written Homework 1
This homework assignment is due in class on Monday, January 27. Show
all work in a legible and understandable manner.
1. Consider the function f (x) =
x2 + 5x 50
.
x5
(a) What is the domain of f ?
(b) Find limx0 f (x
Trigonometry
(1) Given the following right triangle, what are the values ofac and y?
1: ~_ 1.3: gm
8 T5 éll C93 in {BIL-33
3 4
/ y :Lllil/g \EVZ :UlX/a
wwwizféi
I 3 g: :4» "1 m
m l 43 "l 2; ~><
(2) Determine Whether the following trigiiiéiféériémor odd:
Math 3 Day 1 WARMUP
Calculate the given functions at the given mvalues, and then plot the corresponding points.
it) = 162
IE f (33) The Simplest Functions: Lines!
y
b:
y
H
2'31 LE2
Recall: Two points define a line!
Slope: m a: 2 (rise/run)
Point-slope F
Related Rates
(1) A water tank has the shape of an inverted circular cone with base radius 2 m and height
4m. If water is being pumped into the tank at a rate of 2 m3/min, find the rate at which
the water ievei is rising when the water is 3 m deep.
Volume
Position, Velocity, Acceleration Word Problems:
1. An Object dropped from a cliff has acceleration a = 9.8 mls2 under the inuence of gravity.
What is the function s(t) that models its Wat time t? dtxaggg . -
mfg: This quidiriiei {iiiliiipiiiiiifieiidfi gg
Continuity Practice
(1) For which values of x is the function f (x) = x2 + 3x + 4 continuous? Justify your answer
with limits if necessary and draw a graph of the function to illustrate your answer.
(2) For which values of x is the function f (x) =
x2 x6
Trigonometry
(1) Given the following right triangle, what are the values of x and y?
3/4
y
/6
x
(2) Determine whether the following trig functions are even or odd:
f (x) = sin x
f (x) = cos x
f (x) = tan x
f (x) = csc x
f (x) = sec x
f (x) = cot x
(
The Simplest Functions: Lines!
y2
y1
b
x1
x2
Recall: Two points dene a line!
y2 y1
(rise/run)
x2 x1
Point-slope Form: y y1 = m(x x1 )
Slope: m =
Slope-intercept Form: y = mx + b
General Form: Ax + By + C = 0
(good for writing down lines)
(good for graphin