微積分
極限、導數、最優化與函數性質。
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select the correct answer. the graphs represent functions f and g. whic…
D. \( (3,25) \)
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simplify the following expression. assume any factors you cancel are no…
$\frac{8 - k}{k+7}$
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evaluate $f(x) = 5^{x - 1} - 6$ when $x = 9$. a 390,619 b 390,625 c 1,9…
A. 390,619
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this question has several parts that must be completed sequentially. if…
\(-1, -7i, 7i\)
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this question has several parts that must be completed sequentially. if…
$-1, 7i, -7i$
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question 1 of 8 use the drawing tools to form the correct answer on the…
The ordered pair is \((-4,12)\), so we plot the point at \((-4,12)\) on the graph.
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2 select the correct answer. find the value of g(25) for the function b…
B. -336
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question 4 of 5 select the correct answer. if h is a function and -7 is…
The expression \( h(-7) \) represents the output of \( h \) corresponding to the input of \(-7\).
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8. solve: \\(\\frac{3^3 - (2^2 - 1)}{9 \\times 2 \\div 3}\\)
4
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c) the function $f(x) = x^3$, which has been reflected across the $x$-a…
$g(x) = -\frac{1}{2}x^3 + 2$
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question 1-5 select all ordered pairs that represent solutions to the s…
(-1, 8), (3, 0)
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a) the function $f(x) = \\sqrt3{x}$, which has been stretched verticall…
a) $y=5\sqrt[3]{x+2}$ b) $y=2\sqrt{-x}-5$
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120 130 140 150 160 170 180 190 200 210 220 \\(\\begin{array}{r}01\\box…
7
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there is a division operation (dfrac{108}{35}) and some subtraction ope…
3
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9. 5,420 ÷ 61 10. 2,500 ÷ 72
9. $\approx 88.85$ 10. $\approx 34.72$ If exact fractional answers are preferred: 9. $\frac{5420}{61}$ 10. $\frac{625}{18}$
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a) the function $f(x) = sqrt3{x}$, which has been stretched vertically …
$f(x) = 5\sqrt[3]{x+2}$
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simplify the product into a quotient of natural logarithms. \\(\\log_{3…
$\frac{\ln(5)}{\ln(3)}$
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functions - 8.f.2 examine the following sets of functions and determine…
B (or the function \(y = 2x+3\))
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multiple select question select all that apply which statements about n…
- It includes characteristics and behaviors that express meaning without words. - It is a critical part of effective communication. - It includes vocal behaviors, physical appeara…
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solve the following with pen and paper. 9 \\overline{) 8 \\quad 2 \\qua…
9 1 r 7
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fill in the blanks 8 ÷ 3 = r
2 r 2
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which statement primarily appeals to pathos to support the position tha…
If we, as a community, decided to set aside our isolating independence and share many of life's simple tools—such as lawnmowers, bicycles, or Internet connections—we would be far …
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14 longdiv 4 3 4
The filled long division is: ``` 3 1 _______ 14 |4 3 4 4 2 ----- 1 4 1 4 ----- 0 ``` Blanks filled in order (top to bottom, left to right): 3, 1, 4, 2, 1, 4, 1, 4, 0
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add. 2.91 + 30.4
\(33.31\)
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add. 8.5 + 5.16
\( 13.66 \)
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add. 32.64 + 4.5
\(37.14\)
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add. \\begin{array}{r} 53.74 \\\\ +\\ \\ \\ 0.4 \\\\ \\hline \\end{arra…
\(54.14\)
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add. \\begin{array}{r} 26.6 \\\\ +\\ \\ 5.08 \\\\ \\hline \\end{array}
\(31.68\)
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divide. 154÷22
7
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divide. 175 ÷ 35
5
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divide. 207÷23
9
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10. what is a modern example of an authoritarian government? 11. what a…
10. North Korea (a modern state with centralized, non-democratic, authoritarian control over all aspects of society, limited political freedoms, and no free elections) 11. - **Sou…
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what are the domain and range of this function? domain: {x|x ≥ 1}, rang…
domain: $\{x | x \leq 1\}$, range: $\{y | y \leq 0\}$
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what is the range of this function? {y|y > 0} {y|y > 1} {y|y ≥ 0} {y|y …
$\{y|y \geq 0\}$
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4 sketch the graph of each line: $y = \\frac{3}{5}x - 4$
To sketch the graph of \( y=\frac{3}{5}x - 4 \): 1. Plot the y - intercept \( (0,-4) \). 2. Use the slope \( \frac{3}{5} \) to find another point (e.g., from \( (0,-4) \), move 5 …
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3) showing all algebraic steps find the inverse of $f(x) = -\frac{3}{2}…
The inverse relation is \( f^{-1}(x) = -1 \pm\sqrt{\frac{2(6 - x)}{3}} \) (it is a relation, not a function in its full domain). ### Question 4: Is the graph of the inverse a func…
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c) how many points of inflection does the graph of f have? justify your…
The graph of \( f' \) has three points of inflection.
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6 which of the following represents the area of the shaded region in th…
e) \( \int_{a}^{d}[f(y)-a]dy \)
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if \\(\\int_{1}^{3} f(x) dx = 5\\) and \\(\\int_{1}^{6} f(x) dx = 7\\),…
d) 7
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10. if f(x) = e^e, which of the following is f(x)? (a)e^e (b)e^e + 1 (c…
\( \boldsymbol{0} \) (corresponding to option C)
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given the functions $f(x)=x^2 + 4$ and $h(x)=x - 2$, find $(f - h)(-4)$…
26
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u3:04: unit 3 test how can you determine if an inverse is a function? 0…
To determine if an inverse is a function, we can: 1) Apply the horizontal line test to the original function—if no horizontal line intersects its graph more than once (it is one -…
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no calc, no notes part 1. graph ( f(x) = x^2 ), ( f(x) = x^3 ), ( f(x) …
1. - $f(x)=x^2$: Parabola with vertex at $(0,0)$, opening upward, symmetric across the y-axis. - $f(x)=x^3$: Cubic curve passing through $(0,0)$, strictly increasing, symmetric ab…
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elements : pitch & linear pitch review quiz complete inside elements of…
- minor second - semi-tone - half-step
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evaluate + x when x = 1, 15 + x = 15 + 1 =
16
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part b 45.5 - 2.341 43 43.159 43.2 43.16 submit request answer
B. 43.159
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name 8 $6.05 - 1.26
$\$4.79$
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the area labeled b is five times the area labeled a. express b in terms…
\( b = \ln(5e^a - 4) \)
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problem 7: spiral review the graph shows y as a function of x. for whic…
3. From 1 to 3 7. From 5 to 7 (Note: The numbering in the options seems a bit off in the original, but based on the analysis, "From 1 to 3" and "From 5 to 7" are the intervals whe…
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given the following exponential function, identify whether the change r…
Growth, 3.6% increase
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given the following exponential function, identify whether the change r…
This represents exponential growth with a 1% rate of increase.
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given the following exponential function, identify whether the change r…
Growth, 24% increase
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use multiplication and division facts to solve the following problems m…
\( 19 \) ### Problem ②: \( 96 \div 8 \)
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given the following exponential function, identify whether the change r…
Decay, 68% decrease
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given the following exponential function, identify whether the change r…
Growth, 32.5% increase
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evaluate the function for the given value. f(x) = 5 - x for x = -3 f(-3…
8
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evaluate the function for the given value. f(x) = 10x - 15 for x = 5 f(…
35
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0 = \\sqrt3{924 + z} - 12
\(z = 804\)
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select the best description of the following exponential equation. $f(x…
Decaying by 5% with every unit of $x$.
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select the best description of the following exponential equation. $f(x…
Growing by 82% with every unit of $x$.
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23. a digital billboard has an area of 729.6 square feet. what is the p…
The perimeter of the billboard is \( 126.4 \) feet.
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use the parabola tool to graph the quadratic function ( f(x) = x^2 + 10…
Vertex: $(-5, -9)$; Second point: $(0, 16)$ (the parabola opens upward, passing through these points and their symmetric counterparts)
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Question was provided via image upload.
8
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write the equation of the line that passes through the points (-1, 2) a…
$x_2 = 6$, $y_2 = 3$
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use the order of operations to evaluate this expression. enter the numb…
1
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for the function g whose graph is given, state the value of each quanti…
To solve these limit and function value problems, we analyze the graph of \( g(t) \) by examining the left - hand and right - hand behavior as \( t \) approaches a given value, an…
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determine the consecutive integer values of x between which each real z…
D) zero between $x = -2$ and $x = -1$
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read the passage and then answer the question. construction on florence…
blocked
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use the graph of the function to complete the table. input output 2 3 4…
| input | output | |-------|--------| | 2 | 0 | | 3 | -2 | | 4 | 1 |
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given the function below, fill in at least 3 rows of the table of value…
| $x$ | $-\frac{1}{4}x$ | $y = -\frac{1}{4}x - 5$ | |-----|------------------|---------------------------| | $-4$ | $1$ | $-4$ | | $0$ | $0$ | $-5$ | | $4$ | $-1$ | $-6$ |
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the functions u and w are defined as follows.\\(u(x) = 2x - 2\\)\\(w(x)…
$-130$
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the graph shows the relationship between the number of marbles and the …
$v = \frac{1}{2}x + 8$
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match the five definitions to their correct terms. the belief that king…
Divine Right of Kings ### Second Definition (A Protestant Christian denomination...):
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mrs. jacobs and mr. kanavins buy food for an school party. the cost of …
$\$15$
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(int_{0}^{8} \frac{dx}{sqrt{1 + x}})
$2(\sqrt{8} - 1)$ or simplified as $4\sqrt{2} - 2$
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evaluate the function $f(x) = \\frac{x}{|x|}$ at the given values of th…
a. $1$ b. $-1$ c. $1$
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must do activities source: adapted from colin nicolson, the first world…
1. 12,740,000 square miles 2. 17,180,000 square miles 3. 1,139,000 square miles 4. A large colonial population can provide a captive market for the mother country's goods, a low-c…
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what is 15% of 4? x = .75(4) x =
0.6
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1. find the area. use 3.14 for pi and round your answer. 2. divide to s…
The area of the circle is \( 452.16 \, \text{m}^2 \). ### Question 2:
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the equation of line r is $y = \\frac{5}{3}x + 5$. line s is parallel t…
\(\frac{5}{3}\)
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graph the equation y = 3x + 5 use the graphing tool to graph the line
The line $y=3x+5$ is graphed by plotting the y-intercept $(0, 5)$, using the slope to find a second point $(1, 8)$, and drawing a straight line through these points.
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must do activities source: adapted from the cartoon - times memory of t…
12,740,000 square miles #### 2. What was the combined AREA of colonies held by the nations of the Triple Entente? (Great Britain, France & Russia)
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practice 1. carson’s wheelbarrow can hold 345 pounds. if he has 121 pou…
\(p \leq 224\) ### Problem 2
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which of the following things could a company do to encourage innovatio…
C. Reward employees who show creativity and who lead positive changes
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3) average value of a function problem: find the average value of $f(x)…
The average value of the function \( f(x) = 3x^{2}+2 \) on the interval \([1,4]\) is \( 23 \).
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19. the graph of a function ( f ) on the closed interval ( 0, 6 ) is sh…
B. 0
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6.4 accumulation functions 18. let ( g(x) = \frac{d}{dx} int_{0}^{x} sq…
E. 5
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to divide two fractions, we \keep it, change it, flip it\. this means, …
$\frac{5}{6}$, $\frac{5}{4}$, $\frac{25}{24}$
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many problems require you to enter a number or expression in an answer …
5
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Question was provided via image upload.
Function
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hello, and welcome to the orientation section of your course. this set …
1
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value: 2 what is similar about paying with cash and getting a loan? a. …
a. Both ways require you to pay
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f(x) = \\begin{cases} -2x - 4 & \\text{for} & -4 \\leq x < -1 \\\\ 2 & …
The graph consists of: 1. A line segment from $(-4, 4)$ (closed dot) to $(-1, -2)$ (open dot) for $-4 \leq x < -1$ 2. A horizontal line segment from $(-1, 2)$ (open dot) to $(4, 2…
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evaluate the expression ((4 \times 5)^2 - 6 + 3 =)
\(397\)
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use the graph to determine a. open intervals on which the function is d…
a. B. The function is never decreasing. b. A. The function is increasing on the interval(s) $(-5, 5)$ c. The function is never constant.
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f(x) = \\begin{cases} -2x - 7 & \\text{for} & x < -5 \\\\ 3x + 12 & \\t…
The graph consists of two line segments: 1. A line starting at the open point $(-5, 3)$ and extending left through $(-6, 5)$ (for $x < -5$) 2. A line starting at the open point $(…
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give the slope and the y - intercept of the line with the given equatio…
### Slope: A. The slope is $2$. ### Y-intercept: A. The y-intercept is $8$. ### Graph: A straight line passing through points such as $(0, 8)$, $(1, 10)$, and $(-1, 6)$ on the coo…
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graph the following function on the axes provided. $f(x) = \\begin{case…
- For the piece $f(x)=x-1$ ($x\leq-5$): A line with a closed endpoint at $(-5, -6)$, passing through $(-10, -11)$, extending infinitely left. - For the piece $f(x)=x-10$ ($x>5$): …
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graph the following function on the axes provided. $f(x)=\\begin{cases}…
1. For the piece $f(x)=3x+6$ ($-4<x<-1$): Draw a line with open endpoints at $(-4, -6)$ and $(-1, 3)$, connecting the two points. 2. For the piece $f(x)=-2x+2$ ($-1<x<3$): Draw a …
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3. use the graph below to answer a and b. a. what is the slope of the l…
a. $0$ b. $y = -7$