微积分
极限、导数、最优化与函数性质。
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problem. 5 : consider the rational function $f(x) = \\frac{x^2 + 2x}{x^…
\((-2, \frac{1}{2})\) ### Problem 6.1
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problem. 5 : consider the rational function $f(x)=\\frac{x^2 + 2x}{x^2 …
\( x = 2 \) ### Problem 6
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question 1 0.5 pts let ( f(x) ) be a function and let ( f(a) ) be the d…
I and II (the option with "I and II" text, as per the multiple - choice options in the question)
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question 3 let ( f(x) = sqrt{x} ). it can be seen using the definition …
5.02
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question 2 0.5 pts which of the following limits gives the slope of the…
\(\boldsymbol{\lim\limits_{h\to0} \frac{[(2 + h)^{3}-1]-7}{h}}\) (the first option)
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question 1 let $f(x)$ be a function and let $f(a)$ be the derivative of…
I and II
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problem 3 (fill in the blank) : find the derivative of the following fu…
\( \vec{h}'(t) = -5e^{-5t} \hat{i} + (\ln(t) + 1) \hat{j} - \frac{1}{2t\sqrt{t}} \hat{k} \) (or equivalent forms like \( -5e^{-5t} \hat{i} + (\ln(t) + 1) \hat{j} - \frac{1}{2t^{\f…
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solve the following system of equations graphically on the set of axes …
The intersection point (solution) is $(-4, 5)$. To plot: 1. For $y=\frac{1}{2}x+7$: plot $(0,7)$ and $(-4,5)$, draw the line through them. 2. For $5x+2y=-10$: plot $(0,-5)$ and $(…
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solve the following system of equations graphically on the set of axes …
The solution to the system is the intersection point $(1, -7)$. To graph: 1. Plot the line $y=x-8$ using points $(0,-8)$ and $(8,0)$, then draw a line through them. 2. Plot the li…
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solve the following system of equations graphically on the set of axes …
The solution (intersection point) is $(6, 6)$. To plot: 1. For $y=-\frac{1}{6}x+7$: plot $(0,7)$ and $(6,6)$, draw a line through them. 2. For $y=2x-6$: plot $(0,-6)$ and $(3,0)$,…
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solve the following system of equations graphically on the set of axes …
The solution to the system is the intersection point of the two lines: $(5, 2)$ To plot the lines: 1. For $y=\frac{3}{5}x-1$: plot $(0, -1)$ and $(\frac{5}{3}, 0)$, then draw the …
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solve the following system of equations graphically on the set of axes …
The solution (intersection point) is $(-2, 1)$ To graph: 1. For $y=-\frac{5}{2}x-4$, plot $(0, -4)$ and $(-1.6, 0)$, then draw the line through them. 2. For $y=\frac{1}{2}x+2$, pl…
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solve the system of equations graphed on the coordinate axes below. $y …
The solution is $x=-1$, $y=1$, or the ordered pair $(-1, 1)$
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ones sensibilities; suitable for consumption * clear, transparent; read…
palatable ### Second Question ("clear, transparent; readily understood")
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which factors contributed to early americans preference for limited gov…
B. All these answers are correct.
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multiple select question select all that apply what were two of jeffers…
- to support states' rights - to limit the power of the federal government
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exercises 1.3 the fundamental theorem of calculus score: 245/260 answer…
2000
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exercises 1.3 the fundamental theorem of calculus score: 225/260 answer…
\(12\)
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$$\\int_{-3}^{5} f(x) dx = f(5) - f(-3)$$. is this always true, sometim…
sometimes true (corresponding to the option: sometimes true)
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how did nazi rule affect the lives of german people? select three answe…
A. The media was censored to promote only Nazi ideology. B. Nazi propaganda was shown to children. D. Intense nationalism and shows of patriotism were widespread.
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how did the treaty of versailles help pave the way for the nazi party t…
D. by creating resentment and anger among the German people
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the formula for the volume of a cube is $v(s)=s^{3}$ where $s$ is the s…
quadrant I
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exercises 1.3 the fundamental theorem of ca score: 195/260 answered: 20…
$\cos(5) - \cos(4)$
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how did the us congress respond to the signing of the salt ii (strategi…
A. Congress refused to ratify the treaty.
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graph $h(x) = 2\\sin(\\pi x - 3\\pi) - 4$ in the interactive widget. no…
Extremum point: $(-2, -2)$, Midline intersection point: $(0, -4)$
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graph $h(x) = 2\\sin(\\pi x - 3\\pi) - 4$ in the interactive widget. no…
1. Extremum point example: $\boldsymbol{(3.5, -2)}$ (local maximum) or $\boldsymbol{(2.5, -6)}$ (local minimum) 2. Neighbouring midline intersection: $\boldsymbol{(3, -4)}$ To plo…
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exercises 1.3 the fundamenta score: 140/260 answered: 14/26 question 15…
$\frac{9}{2}\pi$
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use the fundamental theorem of calculus to find the \area under curve\ …
573
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given $f(t)=int_{0}^{t}\frac{x^{2}+11x + 30}{1+cos^{2}(x)}dx$ at what v…
$t=-6$
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how did the posting of the \twelve theses\ by students reflect nazi pol…
by supporting only German professors
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exercises 1.3 the fundamental theorem score: 110/260 answered: 11/26 qu…
$x=-3$
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subtract the fractions and reduce to lowest terms. (enter your answer a…
\(7\frac{9}{10}\)
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subtract the fractions and reduce to lowest terms. (enter your answer a…
\(7\frac{9}{10}\)
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nafta can be defined as a means to acquire convenient resources. a unif…
a unification treaty that limits trade barriers.
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select the function f(x)=√x. use the c - slider to change the value of …
A. The transformation is a horizontal shift left $|c|$ units.
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determine whether the following statement is true or false. if the stat…
B. The statement is false, the graph of f is shifted 3 units to the left and 3 units upward.
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write an equation in slope intercept form that passes through the two p…
\( y=\frac{1}{2}x + 2 \)
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add the following fractions and reduce to lowest terms. (enter a reduce…
$\frac{11}{16}$ ### Second Problem: Total Weight of Packages
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write an equation for the function whose graph is shown to the right th…
$y=(x+3)^2 + 1$
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writing equations of a graph write the equation of the line shown. m: s…
\(y=\frac{3}{4}x - 2\) (Wait, no, wait, maybe I made a mistake. Wait, let's re - examine. The line passes through (0, - 2) and (4,1). So slope \(m=\frac{1-(-2)}{4 - 0}=\frac{3}{4}…
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reflections on the coordinate plane the graph of a linear function is s…
0.5
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subtract. 89.8 - 88.35
1.45
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if $f(x) = \\int_{0}^{x} (t^3 + 4t^2 + 7) dt$ then $f(x) = $
$3x^2 + 8x$
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exercises 1.3 the fundamental theorem of calculus score: 60/260 answere…
$\sqrt{x^3 + 8}$
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use transformations of the standard cubic function, f(x)=x³, to graph t…
B. The graph of $f(x) = x^3$ should be vertically shrunk by a factor of $\frac{1}{2}$.
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exercises 1.3 the fundamental theorem of calculus score: 30/260 answere…
$f'(x)=x^5$ $f'(-5)=-3125$
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exercises 1.3 the fundamental theorem of calculus score: 20/260 answere…
$-x^7$
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use transformations of the standard cubic function, f(x)=x³, to graph t…
The graph of $g(x)=x^3 + 4$ is the graph of $f(x)=x^3$ shifted vertically upward by 4 units, passing through key points $(-2,-4)$, $(0,4)$, and $(2,12)$.
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answer the following true or false. let $f(x)=\\int_{3}^{e^{5x}}f(x)dx$…
True
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exercises 1.3 the fundamental theorem of calculus score: 0/260 answered…
True
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use transformations of the standard cubic function, f(x)=x³, to graph t…
The graph of $g(x)=x^3+2$ is the graph of $f(x)=x^3$ shifted vertically upward by 2 units, passing through points $(-2, -6)$, $(-1, 1)$, $(0, 2)$, $(1, 3)$, $(2, 10)$ and followin…
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the main reason yemen ranks lowest in the world in gender equality is b…
women have limited access to education.
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which best illustrates malala yousafzais story? people may be afraid to…
Women's roles and human rights have been limited in some parts of the world.
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how does the constitution protect human rights? by jailing corrupt lead…
by limiting the government
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perry wants to find the decimal equivalent of \\(\\frac{19}{3}\\), so h…
Next three digits: 3, 3, 3
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jacob knows that \\(\\frac{1}{20}\\) means “1 divided by 20.” he uses t…
The top boxes (decimal digits) are 0 and 5, so the quotient is $0.05$. The bottom subtraction boxes are 1 and 0, so we subtract $100$ from $100$. Filled long division: ``` 0 . 0 5…
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enter a digit in each box to complete the division problem. \\\\begin{a…
- Quotient missing digit: 5 - Dividend missing digit: 5 - Final subtraction missing digit: 4 Completed division: ``` 3 1 5 R7 8 |2,5 2 7 -2 4 ----- 1 2 - 8 ----- 4 7 - 4 0 ----- 7…
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Question was provided via image upload.
- Dividend's leading box: 4 - Quotient's units box: 0 - Final remainder box: 5 Filled division: ``` 820 R5 6 |4,925 -48 ---- 12 -12 ---- 05 ```
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what digit is missing from the quotient? (the long - division process f…
2 (Option: 2)
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question 2 find the domain of the function using interval notation. $f(…
$(-\infty, -2) \cup (-2, 4) \cup (4, \infty)$
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what is the physical manifestation of an individuals response to rhythm…
1. 2. Dance 2. 3. Beat
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graph the function ( f(x) = x^2 - 3 ). then use the line tool to draw t…
- The graph of $f(x)=x^2-3$ is an upward-opening parabola with vertex at $(0, -3)$. - The plotted point is $(3, 6)$.
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9. two piecewise functions are shown below: $f(x)= \\begin{cases} 3x - …
C. 54 ### Question 10
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what is the slope of this line? simplify your answer and write it as a …
\(\frac{1}{2}\)
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two piecewise functions are shown below. $h(x)=\\begin{cases}-3x & \\te…
b. 6 ### Problem 9
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the graphs of linear functions f and g are shown below what is the solu…
\( x = 2 \) ### Question 5 (absolute value graph equation)
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which best describes what occurred during the détente era? arms reducti…
arms limitation
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15. if $f(x) = 3x - 2$, what is $f(4)$? \\bigcirc 12 \\bigcirc 16 \\big…
10
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what was joseph stalins goal in creating a command economy? to graduall…
to outproduce capitalist nations
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which of these were included in the salt i (strategic arms limitation t…
a cap on nuclear arms a limit on launch sites
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17. which function has a steeper slope than $y = 2x + 1$? $y = x + 1$ $…
B. $y=3x-2$
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19. if $f(x) = -4x + 9$ and $f(x) = 1$, what is $x$? (options are prese…
2
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b. \\begin{cases} y = x + 5 \\\\ y = 2x + 9 \\end{cases} for $y = x + 5…
### Completed table for $y=x+5$: | $x$ | $y$ | |-----|-----| | $-5$ | $0$ | | $-4$ | $1$ | | $-3$ | $2$ | | $-2$ | $3$ | | $-1$ | $4$ | | $0$ | $5$ | | $1$ | $6$ | | $2$ | $7$ | |…
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which of these were included in the salt i (strategic arms limitation t…
a. a cap on nuclear arms d. a limit on launch sites
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what government regulation was enacted to limit food and material consu…
The government regulation enacted to limit food and material consumption was **rationing** (implemented through ration books/stamps to control the purchase of scarce goods, often …
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what effort was made to increase the food supply and limit government a…
Efforts included promoting Victory Gardens (to increase local food production), implementing food rationing (to manage supply and reduce government aid dependency), and early food…
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question 7 of 10 what is an example of a tariff? a fee a business adds …
B. A tax a government adds to imported goods to make them more expensive
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question 2 of 10 what best describes what a supply chain is? a chain th…
D. A series of trades from the producer to the consumer
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expansion of voters rights over time, many early american limits on vot…
They frequently impeded African-American voting.
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(5) $9\\frac{1}{4}-1\\frac{2}{3}-\\frac{5}{6}$ = (7) $6\\frac{5}{12}-1\…
(a) $1\frac{1}{4}$ (b) $3\frac{1}{3}$ (c) $1\frac{1}{4}$ (d) $\frac{7}{12}$
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(2) $2\\frac{1}{9} - \\frac{1}{2} - \\frac{1}{3}$ (4) $2\\frac{7}{9} - …
(2) $1\frac{5}{18}$ (4) $1\frac{11}{18}$
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if represents a function, only one of the graph choices presented will …
B. The graph that intersects the line $y=-3$ exactly once
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simplify the following fraction: \\(\frac{64}{88}\\)
$\frac{8}{11}$
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this is the graph of an exponential function. write an equation for the…
\( f(x) = 1 \times 2^x \) (or \( f(x) = 2^x \))
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question given $g(x) = 4x - 5$, find $g(3)$.
7
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solve the following system by graphing.\\( \\begin{cases} 2x - y = 8 \\…
C. The solution set is \(\varnothing\).
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find the minimum value of the function $f(x) = 0.6x^2 - 1.5x + 8.1$ to …
\( 7.16 \)
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the functions f and g are defined as follows. $f(x) = \\frac{x^2}{x - 5…
Domain of $f(x)$: $(-\infty,5) \cup (5,\infty)$ Domain of $g(x)$: $(-\infty,8) \cup (8,9) \cup (9,\infty)$
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evaluate the function ( f(x) = \frac{x}{|x|} ) at the given values of t…
a. $1$ b. $-1$ c. $1$
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$-10$
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use the graph to answer the following questions. (a) over which interva…
To solve these problems, we analyze the graph of the function (even though the graph isn't shown, we use typical concepts of polynomial functions): ### Part (a): Intervals where t…
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use the point - slope equation to identify the slope and the coordinate…
The slope of the line is $\frac{1}{2}$ A point on the line is $(1, 4)$
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the function $f(x)$ is defined below. what is the end behavior of $f(x)…
as \(x ightarrow \infty, y ightarrow -\infty\) and as \(x ightarrow -\infty, y ightarrow -\infty\) (the first option in the list of options)
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what did the 1970 revision of the clean air act establish for the criti…
(Assuming the last option, though partially visible, is "ambient air quality standards") The correct option (assuming the last one is "ambient air quality standards") as the 1970 …
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next round! follow the three clues to find a hidden treasure. write eac…
\(3\frac{2}{5}\) (In the boxes, the first box is 3, the numerator box is 2, and the denominator box is 5)
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find the roots and the vertex of the quadratic on a calculator. round a…
Roots: \(-2\) and \(12\) Vertex: \((5, 49)\)
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for what value of ( k ) will ( x + \frac{k}{x} ) have a relative maximu…
\(k = 4\)
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in his argument in favor of starting classes later in the morning, joão…
- Sleep deprivation harms memory. - Overtired teens are more prone to accidents. - Teens dealing from sleep deprivation lose the ability to focus.
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graph the function $f(x) = 3x^2$. plot the vertex. then plot another po…
1. Plot the vertex at $(0, 0)$. 2. Plot the point $(1, 3)$ and its symmetric point $(-1, 3)$. 3. Draw a smooth upward-opening parabola through these points.
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question determine whether the quadratic function shown below has a min…
The function has a maximum value, and the maximum value is 1.