MATH 1500 Fall 2014 Quiz 1D Solutions
x3 16x
. Determine the following limits. If the limit does not exist, state
x2 + 3x 4
whether it tends to , , or neither.
1. Let f (x) =
[4]
(a) lim f (x)
+
x1
x3 16x
.
x1
x1 x2 + 3x 4
The limit is of the form 15/0 an
MATH 1500 Fall 2014 Quiz 2B Solutions
Family Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Given Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Student ID: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Solve
MATH 1500 Fall 2014 Quiz 1C Solutions
x3 9x
. Determine the following limits. If the limit does not exist, state
x2 + x 6
whether it tends to , , or neither.
1. Let f (x) =
[4]
(a) lim f (x)
+
x2
x3 9x
.
x2
x2 x2 + x 6
The limit is of the form 10/0 and th
MATH 1500 Fall 2014 Quiz 2A Solutions
Family Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Given Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Student ID: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Solve
MATH 1500 Fall 2014 Quiz 1B Solutions
x3 x
. Determine the following limits. If the limit does not exist, state
x2 2x 3
whether it tends to , , or neither.
1. Let f (x) =
[4]
(a) lim f (x)
+
x3
x3 x
.
x3
x3 x2 2x 3
The limit is of the form 24/0 and theref
MATH 1500 Fall 2014 Quiz 1A Solutions
x3 4x
. Determine the following limits. If the limit does not exist, state
x2 + x 2
whether it tends to , , or neither.
1. Let f (x) =
[4]
(a) lim f (x)
+
x1
x3 4x
.
x1
x1 x2 + x 2
The limit is of the form 3/0 and the
Page 1 of 4
Math 1500 Midterm Exam
Solutions
Fall 2014
1)a)
b)
Limit
Or
Upon substitution, one gets the form
to
so the limit does not exist but the functional values tend
. The question is: which one?!
The numerator approaches a negative number as
.
The d
MATH 1500 Fall 2014 Quiz 2C Solutions
Family Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Given Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Student ID: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Solve
MATH 1500 Problem Workshop 2 Solutions
1. (a) Direct substitution make the denominator and numerator 0. Therefore we do some
algebra rst.
( t + 3 2)( t + 3 + 2)
t+32
t1
= lim
lim
= lim
t1 (t 1)(t + 1)( t + 3 + 2)
t1
t1 (t 1)(t + 1)( t + 3 + 2)
t2 1
1
1
1
MATH 1500 Problem Workshop 3 Solutions
1. (a) Here we factor out the biggest term in the numerator and denominator since its
a limit at innity.
g 2 (3 + 4/g)
3g 2 + 4g
= lim 2
lim
g g (5 4/g 2 )
g 5g 2 4
(3 + 4/g)
3+0
3
= lim
=
= .
g (5 4/g 2 )
50
5
(b) P
MATH 1500 Fall 2014 Quiz 2D Solutions
Family Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Given Name: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Student ID: ttttttttttttttttttttttttttttttttttttttttttttttttttttttttt
Solve
MATH 1500 Fall 2014 Quiz 3A Solutions
Solve each of the following questions. Show all work.
[8] 1. Suppose y is a function of x dened inplicitly by
ey + xy 2 = tan(xy).
Determine dy/dx.
Solution: Taking derivatives of both sides gives
dy
dy
+ y 2 + x 2y
d