CALCULUS:EARLY TRANS W/WEB ASSIGN CARD
9th Edition
ISBN: 9780357466278
Author: Stewart
Publisher: CENGAGE L
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Chapter B, Problem 38E
To determine
The slope and
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Question
Is the function f(x) shown in the graph below continuous at x = -5?
f(z)
7
6
5
4
2
1
0
-10
-6 -5
-4
1
0
2
3
5
7
10
-1
-2
-3
-4
-5
Select the correct answer below:
The function f(x) is continuous.
The right limit exists. Therefore, the function is continuous.
The left limit exists. Therefore, the function is continuous.
The function f(x) is discontinuous.
We cannot tell if the function is continuous or discontinuous.
The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = -1.
654
-2-
-7-6-5-4-
2-1
1 2
5 6 7
02.
Select all that apply:
☐ f(x) is not continuous at x = -1 because f(-1) is not defined.
☐ f(x) is not continuous at x = −1 because lim f(x) does not exist.
x-1
☐ f(x) is not continuous at x = −1 because lim ƒ(x) ‡ ƒ(−1).
☐ f(x) is continuous at x = -1
J-←台
Let h(x, y, z)
=
—
In (x) — z
y7-4z
-
y4
+ 3x²z — e²xy ln(z) + 10y²z.
(a) Holding all other variables constant, take the partial derivative of h(x, y, z) with
respect to x, 2 h(x, y, z).
მ
(b) Holding all other variables constant, take the partial derivative of h(x, y, z) with
respect to y, 2 h(x, y, z).
Chapter B Solutions
CALCULUS:EARLY TRANS W/WEB ASSIGN CARD
Ch. B - Prob. 1ECh. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Prob. 11ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Prob. 25ECh. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50ECh. B - Prob. 51ECh. B - Prob. 52ECh. B - Prob. 53ECh. B - Prob. 54ECh. B - Prob. 55ECh. B - Prob. 56ECh. B - Prob. 57ECh. B - Prob. 58ECh. B - Prob. 59ECh. B - Prob. 60ECh. B - Prob. 61E
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- ints) A common representation of data uses matrices and vectors, so it is helpful to familiarize ourselves with linear algebra notation, as well as some simple operations. Define a vector ♬ to be a column vector. Then, the following properties hold: • cu with c some constant, is equal to a new vector where every element in cv is equal to the corresponding element in & multiplied by c. For example, 2 2 = ● √₁ + √2 is equal to a new vector with elements equal to the elementwise addition of ₁ and 2. For example, 問 2+4-6 = The above properties form our definition for a linear combination of vectors. √3 is a linear combination of √₁ and √2 if √3 = a√₁ + b√2, where a and b are some constants. Oftentimes, we stack column vectors to form a matrix. Define the column rank of a matrix A to be equal to the maximal number of linearly independent columns in A. A set of columns is linearly independent if no column can be written as a linear combination of any other column(s) within the set. If all…arrow_forwardThe graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = 3. Select all that apply: 7 -6- 5 4 3 2 1- -7-6-5-4-3-2-1 1 2 3 4 5 6 7 +1 -2· 3. -4 -6- f(x) is not continuous at a = 3 because it is not defined at x = 3. ☐ f(x) is not continuous at a = - 3 because lim f(x) does not exist. 2-3 f(x) is not continuous at x = 3 because lim f(x) ‡ ƒ(3). →3 O f(x) is continuous at a = 3.arrow_forwardIs the function f(x) continuous at x = 1? (z) 6 5 4 3. 2 1 0 -10 -9 -7 -5 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Select the correct answer below: ○ The function f(x) is continuous at x = 1. ○ The right limit does not equal the left limit. Therefore, the function is not continuous. ○ The function f(x) is discontinuous at x = 1. ○ We cannot tell if the function is continuous or discontinuous.arrow_forward
- Is the function f(x) shown in the graph below continuous at x = −5? f(x) 7 6 5 4 2 1 0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 Select the correct answer below: The function f(x) is continuous. ○ The right limit exists. Therefore, the function is continuous. The left limit exists. Therefore, the function is continuous. The function f(x) is discontinuous. ○ We cannot tell if the function is continuous or discontinuous.arrow_forward4. Evaluate the following integrals. Show your work. a) -x b) f₁²x²/2 + x² dx c) fe³xdx d) [2 cos(5x) dx e) √ 35x6 3+5x7 dx 3 g) reve √ dt h) fx (x-5) 10 dx dt 1+12arrow_forwardMath 2 question. thxarrow_forward
- Please help on this Math 1arrow_forward2. (5 points) Let f(x) = = - - - x² − 3x+7. Find the local minimum and maximum point(s) of f(x), and write them in the form (a, b), specifying whether each point is a minimum or maximum. Coordinates should be kept in fractions. Additionally, provide in your answer if f(x) has an absolute minimum or maximum over its entire domain with their corresponding values. Otherwise, state that there is no absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute maxima and minima respectively.arrow_forwardLet h(x, y, z) = — In (x) — z y7-4z - y4 + 3x²z — e²xy ln(z) + 10y²z. (a) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to x, 2 h(x, y, z). მ (b) Holding all other variables constant, take the partial derivative of h(x, y, z) with respect to y, 2 h(x, y, z).arrow_forward
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