PRECALCULUS VOL. 1 W/ENH. WEBASSIGN >I
7th Edition
ISBN: 9781305771642
Author: Stewart
Publisher: CENGAGE C
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Chapter 9.4, Problem 12E
To determine
To find: The magnitude of the
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Is the function f(x) continuous at x = 1?
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-10 -9
-8 -7
-6
-5
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-1 0
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-1
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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.
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
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-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
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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
Chapter 9 Solutions
PRECALCULUS VOL. 1 W/ENH. WEBASSIGN >I
Ch. 9.1 - (a) A vector in the plane is a line segment with...Ch. 9.1 - (a) The length of a vector w = a1, a2 is | w | =...Ch. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 5ECh. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 7ECh. 9.1 - Sketching Vectors Sketch the vector indicated....Ch. 9.1 - Prob. 9ECh. 9.1 - Prob. 10E
Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Sketching Vectors Sketch the given vector with...Ch. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Writing Vectors in Terms of i and j Write the...Ch. 9.1 - Operations with Vectors Find 2u, 3v, u + v, and 3u...Ch. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Velocity A river flows due south at 3 mi/h. A...Ch. 9.1 - Velocity Suppose that in Exercise 55 the current...Ch. 9.1 - Velocity The speed of an airplane is 300 mi/h...Ch. 9.1 - Velocity A migrating salmon heads in the direction...Ch. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - True Velocity of a Jet Find the true speed and...Ch. 9.1 - True Velocity of a Jet In what direction should...Ch. 9.1 - Prob. 63ECh. 9.1 - Velocity of a Boat The boater in Exercise 63 wants...Ch. 9.1 - Prob. 65ECh. 9.1 - Velocity A woman walks due west on the deck of an...Ch. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Prob. 68ECh. 9.1 - Prob. 69ECh. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Equilibrium of Forces The forces F1, F2, , Fn...Ch. 9.1 - Equilibrium of Tensions A 100-lb weight hangs from...Ch. 9.1 - Equilibrium of Tensions The cranes in the figure...Ch. 9.1 - DISCUSS: Vectors That Form a Polygon Suppose that...Ch. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - Prob. 19ECh. 9.2 - Perpendicular Vectors? Determine whether the given...Ch. 9.2 - Dot Products Find the indicated quantity, assuming...Ch. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Dot Products Find the indicated quantity, assuming...Ch. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Projection Show that projv u and u projv u are...Ch. 9.2 - Projection Evaluate v projv u.Ch. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Work A car drives 500 ft on a road that is...Ch. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.2 - Prob. 53ECh. 9.3 - The distance between the point P(x1, y1, z1) and...Ch. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Center and Radius of a Sphere Show that the...Ch. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Trace of a Sphere In these exercises we find the...Ch. 9.3 - Spherical Water Tank A water tank is in the shape...Ch. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.4 - A vector in three dimensions can be written in...Ch. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Prob. 29ECh. 9.4 - Prob. 30ECh. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Angle Between Two Vectors Find the angle between u...Ch. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Direction Angles of a Vector Find the direction...Ch. 9.4 - Direction Angles of a Vector Find the direction...Ch. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 45ECh. 9.4 - Prob. 46ECh. 9.4 - Parallel Vectors Two nonzero vectors are parallel...Ch. 9.4 - Prob. 48ECh. 9.4 - Prob. 49ECh. 9.4 - Prob. 50ECh. 9.4 - Prob. 51ECh. 9.5 - The cross product of the vectors u = a1, a2, a3...Ch. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Orthogonal Vectors Two vectors u and v are given....Ch. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Area of a Parallelogram Find the area of the...Ch. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.5 - Rubiks Tetrahedron Rubiks Cube, a puzzle craze of...Ch. 9.5 - Prob. 37ECh. 9.6 - A line in space is described algebraically by...Ch. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Prob. 11ECh. 9.6 - Equations of Lines Find parametric equations for...Ch. 9.6 - Prob. 13ECh. 9.6 - Prob. 14ECh. 9.6 - Prob. 15ECh. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Equations of Lines A description of a line is...Ch. 9.6 - Prob. 29ECh. 9.6 - Prob. 30ECh. 9.6 - Prob. 31ECh. 9.6 - Equations of Planes A description of a plane is...Ch. 9.6 - Prob. 33ECh. 9.6 - Prob. 34ECh. 9.6 - DISCOVER: Intersection of a Line and a Plane A...Ch. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9 - Prob. 1RCCCh. 9 - Prob. 2RCCCh. 9 - Prob. 3RCCCh. 9 - (a) Describe the three-dimensional coordinate...Ch. 9 - Prob. 5RCCCh. 9 - Prob. 6RCCCh. 9 - Prob. 7RCCCh. 9 - Prob. 8RCCCh. 9 - Prob. 9RCCCh. 9 - Prob. 10RCCCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - True Velocity of a Plane An airplane heads N 60 E...Ch. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Finding an Equation of a Sphere Find an equation...Ch. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - A river is flowing due east at 8 mi/h. A man heads...Ch. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Calculate the given quantity if u = i + j 2k v =...Ch. 9 - Find two unit vectors that are perpendicular to...Ch. 9 - (a) Find a vector perpendicular to the plane that...Ch. 9 - Prob. 11TCh. 9 - Prob. 1PCh. 9 - Prob. 2PCh. 9 - Prob. 3PCh. 9 - Prob. 4PCh. 9 - Prob. 5PCh. 9 - Prob. 6PCh. 9 - Prob. 7PCh. 9 - Prob. 8PCh. 9 - Prob. 9PCh. 9 - Prob. 10PCh. 9 - Prob. 11PCh. 9 - Prob. 12PCh. 9 - Prob. 13PCh. 9 - Prob. 14PCh. 9 - Prob. 15PCh. 9 - Prob. 16PCh. 9 - Prob. 17PCh. 9 - Match the vector field F with the graphs labeled...Ch. 9 - Prob. 19P
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- 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).arrow_forwardints) 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_forward
- Is 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_forwardIs 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_forward
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