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Elementary,Middle School,High School,College,University,PHD
Teaching Since: | Apr 2017 |
Last Sign in: | 229 Weeks Ago, 5 Days Ago |
Questions Answered: | 12843 |
Tutorials Posted: | 12834 |
MBA, Ph.D in Management
Harvard university
Feb-1997 - Aug-2003
Professor
Strayer University
Jan-2007 - Present
Alexa Fallon
Assignment Homework1 due 06/05/2017 at 11:59pm EDT Summer2017-Math1120-001 Answer(s) submitted: 1. (1 point) • 14x+13 Which of the following graphs represent y as a function of x? (correct)
3. (1 point) Let f (x) = 3 − 4x and g(x) = 3x + 4x2 . Evaluate each of the following:
f (−9) =
g(−6) =
f (−6) + g(−6) =
g(−9) − f (−6) =
f (−6) · g(−3) =
f (−9)
=
g(−3)
Answer(s) submitted:
•
•
•
•
•
• 39
126
153
270
729
39/27 (correct)
4. (1 point)
The graph of a function f is shown below. Select the letters of the graphs that do represent y as a function
of x.
• A. A
• B. B
• C. C
• D. D
• E. E
• F. F
• G. None of the above Use the given graph of f . If there is more than one answer to a
question, you can use commas and the word “or”. When solving an equation for the variable x, your answer should be in the
form “x=\ \ \ ”. Answer(s) submitted:
• a. Evaluate f (0).
f (0) = ( A, B, C ) (correct)
2. (1 point) Express the rule ”Multiply by 14, then add b. Solve f (x) = −2. 13” as the function
Answer(s) submitted: f (x) = . • 0
• x=-2
1 (correct)
8. (1 point) 5. (1 point)
Fill in the blanks.
If H(5) = 3, then the point
is on the graph of H.
If (3, 5) is on the graph of H, then H(3) =
.
Answer(s) submitted:
• (5,3)
• 5 (correct) 6. (1 point) Part 1 of 2: (After you have submitted Match the Lines L1 (blue), L2 ( red) and L3 (green) with the
slopes by placing the letter of the slopes next to each set listed
below: correct answer(s), advance to the next part by selecting Go on
to next part and clicking Submit Answers again.) 1. The slope of line L3
2. The slope of line L2
3. The slope of line L1 x
Suppose f (x) =
.
x
−
1
4
(a) f
help (formulas)
=
t
4
(b) f
=
help (formulas)
t +4
(c) Solve f (x) = 4.
x=
help (numbers) A. m = 0
B. m = −1.7
C. m = 0.5
Answer(s) submitted:
• a
• c
• b Answer(s) submitted:
• (4/t)/((4/t)-1)
•
• 4/3 (correct)
9. (1 point) (score 0.4000000059604645) What is the slope of the line through (3, -6) and (3,7)? If the
slope is undefined, type undefined . 7. (1 point) What is the slope of the line through (6, 1) and (-9,1)? If the
slope is undefined, type undefined . (Error: Unexpected character ’´; see position 1 of formula ’ =12 =12
Find the slope of the line y = 2 − 10x. What is the slope of the line through (-9, 3) and (-4,-6)? If the
slope is undefined, type undefined . Answer(s) submitted:
Answer(s) submitted: • -10 • undefined
• 0/-6
• -1.8 (correct) (correct)
2 10. (1 point) The equation of the line that goes through the point (4, 4) and is parallel to the line going through the
points (−2, 1) and (3, 3) can be written in the form y = mx + b
where
m is:
and b is:
Answer(s) submitted:
• 2/5
• 2.4 (correct)
11. (1 point) The next few questions will rein- As x gets closer and closer to (but stays less than) 1, g(x) gets as
close as we want to
.
As x gets closer and closer to (but stays greater than) 1, g(x) gets
.
as close as we want to
As x gets closer and closer (but not equal) to 1, does g(x) get as
close as we want to a single value? If such a value exists, enter
it. If no such value exists, enter DNE.
.
x= force your mastery of the Cartesian Coordinate System and of
equations of straight lines. The distance between two points
is obtained by the Pythagorean Theorem. The distance of a
point P from a line L is the shortest distance between that point
and a point on the line. Geometrically, you can obtain it by
drawing a line through P perpendicularly to L. It will intersect
L in a point Q which is the point on L closest to P. Once you
have Q you simply compute the distance h between P and Q.
These concepts are illustrated in this Figure: Answer(s) submitted:
• 4
• 2
• dne (score 0.6666666865348816)
13. (1 point)
Determine lim f (x) for the function f (x) shown in the figure
x→5 below We will build slowly to a general formula for the distance of P
from L. Let’s start with the line L defined by
1
y = x + 1.
2
The slope of L is
y=
.
A line that’s perpendicular to L has the slope
.
Hint: The slopes of two lines are negative reciprocals of each
other.
Answer(s) submitted:
• 1/2
• -2 The limit as x → 5 is (correct)
12. (1 point) Answer(s) submitted:
• 3 Suppose that g is the function given by the graph below. Use the graph to fill in the blanks in the following
sentences. (correct)
3 help (limits) (correct)
14. (1 point) Use the given graphs of the function f (left, in blue) and g (right, in red) to find the following limits: 17. (1 point) Evaluate the limit
lim 1 + 10x x→7 2
1 − 7x Enter DNE if the limit does not exist.
Limit =
Answer(s) submitted:
• 5041/2304 1. lim [ f (x) + g(x)] =
x→1 help (limits) (correct) 2. lim [ f (x) + g(x)] =
x→2 18. (1 point) 3. lim f (x)g(x) = Evaluate the limit x→0 f (x)
=
x→0 g(x)
p
5. lim 3 + f (x) = t 2 − 36
t→6 4t 2 − 16t − 48 4. lim lim x→−1 Note: You can click on the graphs to enlarge the images. Enter DNE if the limit does not exist.
Limit = Answer(s) submitted: Answer(s) submitted: • 3
•
• 0
• dne
• • 12/32 (correct)
19. (1 point) Evaluate the limit (incorrect)
x2 + 3x − 18
x→3
x−3 15. (1 point) lim Sketch the following function and use it to determine the values
of a (list in ascending order below) for which lim f (x) does not
x→a
exist: 2−x x
f (x) = (x − 1)2 Enter I for ∞, -I for −∞, and DNE if the limit does not exist. if x < −1
if − 1 ≤ x < 1
if x ≥ 1 Answer(s) submitted:
• 9 (correct) a=
a= 20. (1 point)
the limit Answer(s) submitted:
•
•
3
lim x 8 +
x→0
x (incorrect)
Answer: 16. (1 point)
Evaluate the limit assuming that lim g(x) = −8: Answer(s) submitted: x→3 lim g(x)
2
x→3 x Reduce the expression and then evaluate • 3 = (correct) Answer(s) submitted:
• -8/9
4 • 21. (1 point) Evaluate the limits. 2 3x − 6 x < −1
f (x) = 3x3 + 6 −1 ≤ x ≤ 1 2
3x + 6 x > 1 (incorrect)
23. (1 point) Evaluate the limit
lim x→∞ (9 − x)(2 + 7x)
(3 − 9x)(8 + 11x) Enter DNE if the limit does not exist.
a) lim f (x) =
x→−1− b) lim f (x) = Answer(s) submitted:
• 7/99 c) lim f (x) = (correct) d) f (−1) =
e) lim f (x) = 24. (1 point) x→−1+ x→−1 A function is said to have a horizontal asymptote if either the
limit at infinity exists or the limit at negative infinity exists.
Show that each of the following functions has a horizontal
asymptote by calculating the given limit.
−7x
=
lim
x→∞ 8 + 2x
2x − 9
=
lim
x→−∞ x3 + 4x − 13
2
x − 10x − 12
=
lim
x→∞ √12 − 14x2
2
x + 8x
=
lim
x→∞ 3√
− 15x
x2 + 8x
lim
=
x→−∞ 3 − 15x x→1− f) lim f (x) =
x→1+ g) lim f (x) =
x→1 h) f (1) =
Answer(s) submitted:
• -3
• 3
• 9
• 3
• 9
• 9
• 9
• 9 (score 0.875) Answer(s) submitted:
• -7/2
• 0
• -1/14
• -1/15
• 1/15 22. (1 point)
The signum (or sign) function , denoted by sgn, is defined by −1 if x < 0 0
if x = 0
sgn x = 1
if x > 0 (correct)
25. (1 point) Find each of the following limits.If the limit does not exist, enter
DNE below.
(a) lim sgn x = Let P and Q be polynomials.
P(x)
Find lim
x→∞ Q(x)
if the degree of P is (a) less than the degree of Q, and (b) greater
than the degree of Q. If the answer is infinite, enter ”I” below.
(a)
(b) x→0+ (b) lim sgn x =
x→0− (c) lim sgn x =
x→0 (d) lim |sgn x| =
x→0 Answer(s) submitted:
•
• Answer(s) submitted:
•
•
• (incorrect) c
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