Math 116 - Lab 5 - Fall 2011.
Applications of derivatives: related rates; minima and maxima of a function; Mean Value
theorem (Sections 3.4, 4.2, 4.4 and 4.5 of L/G).
You are to provide full solutions to the following problems. You are allowed to collabor
Math 116 - Lab 3 - Fall 2011.
Rules for dierentiation, chain rule, derivatives of trig, exponential, hyperbolic, inverse
trig and inverse hyperbolic functions (Sections 3.3, 3.5-3.7 of L/G).
You are to provide full solutions to the following problems. You
MATH 116 137 Calculus 1, Assignment 5
Due Thu Oct 23
1: (a) Let f (x) = 5 x2 . Using the denition of the derivative as a limit, nd f (2) and
then nd the equation of the tangent line to the curve y = f (x) at the point where x = 2.
(b) Let f (x) = x3 + x 1
Math 116 - Lab 9 - Fall 2011.
Integration by Substitution, Average Value of a Function, Curve Length (Sections 6.1, 7.7
and 7.1 of L/G).
You are to provide full solutions to the following problems. You are allowed to collaborate with your
classmates, use
Math 116 - Lab 9 Solutions - Fall 2011.
1. Compute the following integrals by substitution.
a) I = sin(3x) dx.
We can use the substitution u = 3x, which gives du = u (x)dx = 3dx and thus
du/3 = dx, so I = sin(u)/3 du = cos(u)/3 + c = cos(3x)/3 + c.
b) I =
Math 116 - Lab 10 - Fall 2011.
Volumes of Solids of Revolution (methods of disks, washers, and spherical shells); Work,
Energy, Force (Sections 7.2, 7.3 and 7.4 of L/G).
You are to provide full solutions to the following problems. You are allowed to colla
Math 116 - Lab 10 Solutions - Fall 2011.
1. Use the method of disks to compute the volume of the solid of revolution generated
by the following areas:
a) Between y = 8 x/2, y = 2, y = 5, and x = 0; about x = 0.
1
b) Between y = 4x x3 , x = 0, x = 2, and y
Math 116 - Lab 11 - Fall 2011.
Center of Mass, Hydrostatic Force (Sections 7.5 and 7.6 of L/G).
You are to provide full solutions to the following problems. You are allowed to collaborate with your
classmates, use your notes and textbook and ask the TA fo
MATH 116 - Lab 11 - Solutions
1. For the following lamina, compute i) the mass of the lamina, ii) the rst moment of
the lamina with respect to the y -axis, iii) the rst moment of the lamina with respect
to the x-axis, iv) the center of mass of the lamina.
Minor corrections to the solution of #6 a) and 12 a) of Lab #5.
6 a) The student should note that the presented solution assumes that b > 0. For a complete solution we
should also answer the question for the cases where b = 0 and b < 0.
12 a) The given so
Math 116 - Lab 1 - Fall 2011.
Functions: exponential, trig, inverses, log, unit-step, hyperbolic (Sections 1.4-1.8 of L-G).
You are to provide full solutions to the following problems. You are allowed to collaborate with your
classmates, use your notes an
MATH 116: Assignment 4 Solutions
due Monday, October 6, 2014 at 3:00pm
t
mg
1. The velocity of a falling skydiver can be modelled by v(t) =
1 e m where
m is the mass of the skydiver, g is the acceleration due to gravity, is the air drag
coecient, and t is
MATH 116: Assignment 5 Solutions
NOT due
1. Use the differentiation rules to find derivative of each function:
xix/1 - x2 . _1 1
(a) N11?) 2 (b) 33) : tan(351n 33) (C) f(5)
Solution:
(a)
3 (CH:5)2
(b) f/(l) : sec2 (3 sin1 ~
A, w 0- (s + he) - (1
Math 116: Assignment 7 Solutions
due Monday, November 3, 2014 at 3:00 pm
1. Find all critical numbers of the given functions.
(a) f (x) = 2x3 30x2 + 144x + 17 (b) h(p) = pp+1
2 4
Solution:
(a) f (x) = 6x2 60x + 144 = 6(x2 10x + 24) = 6(x 4)(x 6). The deri
MATH 116: Assignment 3 Solutions
due Monday, September 29, 2014 at 3:00pm
1. Let h(x) be the Heaviside function, dened (as in the textbook) as:
h(x) =
0
1
if x < 0
.
if x > 0
(a) Write the function f (x) = x+(1x)h(x1)+(4xx2 4)h(x2) in piecewise-dened
form
Math 116: Assignment 8 Solutions
due Monday, November 10, 2014 at 3:00 pm
1. Two posts, one 12 feet high and one 28 feet high, stand 30 feet apart. A single stake is
to be placed in the ground between them, with wires attaching the top of each post to the
Math 116 Midterm Exam
Fall 2014
Qatéélm m*
Last Name
First Name
Email
Student ID W Section
Instructor Section Division Instructor Section Division
A. Beltaos 001 (CHE) F. Dunbar 005 (ME)
M. Alwan 002 (GIVE) F. Girelii 006 (Mechatronics)
E. Dupont 003 (GEO