微积分
极限、导数、最优化与函数性质。
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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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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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use transformations of the standard cubic function, f(x)=x³, to graph t…
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: 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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identify the graph of this rational function. $y = \\frac{5}{x^2 - 1}$
The second graph (the one with the two upper curves above the horizontal asymptote (y = 0) for $x>1$ and $x < - 1$, and the lower curve below the horizontal asymptote passing thro…
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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. a cap on nuclear arms d. 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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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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the function $f(x)$ is defined below. what is the end behavior of $f(x)…
as \( x ightarrow \infty, f(x) ightarrow \infty \) and as \( x ightarrow -\infty, f(x) ightarrow -\infty \) (the first option in the choices)
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follow the three clues to find a hidden treasure. use the number line s…
$2\frac{5}{8}+\frac{7}{8}=\boldsymbol{3}\frac{\boldsymbol{4}}{\boldsymbol{8}}$ (or $3\frac{1}{2}$ if simplifying $\frac{4}{8}$, but based on the number line with eighths, $3\frac{…
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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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on the set of axes below, solve the following system of equations graph…
The solution set is \(\{(-5,2),(-3,-2)\}\) (assuming the second equation is \(y = - 2x-8\) instead of \(y=-2x - 3\) due to the graph's vertex and the need for real intersections)
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what is the slope of this line? simplify your answer and write it as a …
\(\frac{4}{7}\)
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write \\(\frac{57}{25}\\) as a decimal.
\(2.28\)
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find the average rate of change of $f(x)=3x^2 + 2$ from $x = 2$ to $x =…
18
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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.
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when the area in square units of an expanding circle is increasing twic…
\(\frac{1}{\pi}\)
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check here for instructional material to complete this problem. perform…
\(4\)
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simplify your answer and write it as a proper fraction, improper fracti…
$-\frac{2}{3}$
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$-10$
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(int_{0}^{8} \frac{dx}{sqrt{1 + x}})
\( 4 \)
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y = x + 4\ y = 3x\ (grid coordinate system graph)\ solution:______
$(2, 6)$
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how many solutions are there to the system of equations?\\\\begin{cases…
no solutions
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which function rule matches the table? $f(x)=3 - x^3$ $f(x)=9 - 5x$ $f(…
\( f(x)=3 - x^{2} \)
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3. consider the graph of g, shown below. a. state the intervals on whic…
a. $(-2, 0)$ and $(2, \infty)$ b. $(-\infty, -2)$ and $(0, 2)$ c. $(-2, -1)$ and $(2, 0)$ d. $(0, 2)$ e. $(-\infty, -1)$ and $(1, \infty)$ f. $(-1, 1)$ g. $(-1, 0)$ and $(1, 1)$
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evaluate the definite integral.\\(\\int_{1}^{6} 2 \\, dx = \\square\\)
\( 10 \)
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how many solutions are there to the system of equations ( y = \frac{2}{…
There are 0 solutions. The two lines have identical slopes ($\frac{2}{3}$) but different y-intercepts, so they are parallel and never cross, resulting in no common solution points.
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(int left( \frac{3x^3 - 4x - 2}{x^3} ight) dx = square + c)
\(3x+\frac{4}{x}+\frac{1}{x^{2}}+C\)
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2. you are given the graph of $y = -\frac{1}{3}x - 6$ and $y = \frac{1}…
There is 1 solution to this system. Wait, correction: No, visually the lines do not intersect, so 0 solutions. Wait, let's check algebraically: Set $-\frac{1}{3}x -6 = \frac{1}{5}…
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int t^{4} dt = square + c
$\frac{t^5}{5}$
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describing composite functions the volume, in cubic feet, of a right cy…
- The domain of $V(h(r))$ is restricted to values of $r$ greater than 0. - $V(h(r)) = 3.5\pi r^3$ Wait, but the problem says "choose three"—wait, no, I must have misread. Wait, is…
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lena wants to tile her kitchen floor, which has an area of 131 square f…
27 packs of tiles
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y = -x² - 1 which statement is true about the function? ○ when x is neg…
\(y\lt0\) for all values of \(x\)