微积分
极限、导数、最优化与函数性质。
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simplify the following rational function: $f(x) = \\frac{x+4}{x^2+4x}$ …
$f(x)=\frac{1}{x}$
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find the slope of the line graphed below.
$\frac{-5}{3}$
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divide. give the exact answer, written as a decimal. $39.611 \\div 0.10…
380.875
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which graph description best matches:$f(x) = \\frac{x-1}{x^3}$○ a verti…
A. A vertical asymptote at $x = 0$ and an x-intercept at $x = 1$
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divide. give the exact answer, written as a decimal. $44.041 \\div 0.03…
1376.28125
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divide. give the exact answer, written as a decimal. $\\dfrac{51.15}{0.…
68.2
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determine the domain on which the following function is decreasing.
The function is decreasing on the interval $(5, 14)$ or $5 < x < 14$
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find the slope of the line graphed below.
$\frac{3}{4}$
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e 4 - (2 - 15)
17
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what is the domain of the graph? what is the range of the graph? true o…
1. Domain: $\boldsymbol{-5 \leq x < 3}$ 2. Range: $\boldsymbol{-7 \leq y \leq 0}$ 3. False 4. d) The graph was stretched by a factor of 5
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h (-4 + 9) · -3
-15
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(h) $(-4 + 9) - (-3)$
2
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what is the inverse of $y = \\frac{x - 9}{5}$? use algebraic notation t…
1. Inverse function: $y = 5x + 9$ 2. Transform black $y=x^2$: shift left 4 units, then down 7 units to get $y=(x+4)^2-7$ 3. Local maximum: the top-left square (near the positive y…
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find $12.48 + (-10.636)$. write your answer as $12.48 + (-10.636) = \\s…
1.844
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a mound of sand at a rock-crushing plant is growing over time. the equa…
D. 14 hours
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values from the function $g(x)=2\\sqrt3{x+3}-1$ are shown in the table.…
$x=-3$
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the graph of $y = f(x)$ and $y = 4$ is shown. what is the value of $x$ …
$x=3$
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solve: $2\\sqrt3{3x - 1} - 6 = -2$ $x = \\square$
$x = 3$
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what is a commodity? a. something that producers are unable to sell to …
D. Something of value that can be bought, sold, or traded.
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in capitalism, what does competition do for consumers? a. it limits the…
D. It keeps prices fair for consumers.
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e $(-8 cdot -3) - 5$
19
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test prep evaluate the expression. $13 - 2 \\times 5 + 7^2$ show hints …
52 (corresponding to the last option: 52)
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$40 - 4^{2} \\times 2 + 1 = \\square$ options: 7, 8, 9, 4, 5, 6
9
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evaluate the expression. enter the correct answer in the box. show hint…
68
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evaluate the expression. enter the correct answer in the box. show hint…
18
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find the missing number to make the equation true. $7 + 8 + \\underline…
10
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13. graph: $y = -x$
A straight line passing through the origin $(0,0)$, $(2,-2)$, and $(-2,2)$, sloping downward from left to right across the coordinate grid.
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use the graph of the function f to decide whether each quantity exists.…
(a) $4$ (b) $6$ (c) $\text{DNE}$ (d) $4$
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the movement of the progress bar may be uneven because questions can be…
$\log_{4}100 \approx 3.3$
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consider the following function. $f(x)=\\frac{1}{x-8}$ determine whethe…
(a) $-\infty$ (b) $+\infty$ (or $\infty$)
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consider the following function. $f(x) = 6x - 9$ find the limit. $lim_{…
6
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find and write the missing number to make the equations true. 6. $4 + 8…
6. $7$ 7. $7$ 8. $3$ 9. $20$ 10. $16$
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a function $f$ is continuous on the closed interval $-2, 5$, differenti…
D. None of the above
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set f write the missing number to make equation true. $14 + 6 = \\_\\_\…
8
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title dear reader, where do you want to go in life? how do you plan to …
1. the lessons about resisting corrupting power from Frodo's journey in Middle-earth 2. *The Burden of Power: Lessons from Mordor* 3. share cautionary lessons about corrupting pow…
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understanding exponential decay functions which statements are true abo…
The function has a constant multiplicative rate of change The base must be less than 1 and greater than 0. The domain is all real numbers.
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graph this function. $y = 8(0.5)^x$ plot two points to graph the functi…
Plot the points $(0, 8)$ and $(1, 4)$ (or other valid pairs like $(2, 2)$) on the grid, then draw a smooth decreasing curve through them that approaches the x-axis as $x$ increase…
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find the missing number in the equation collects on sunday. $12 + 29 + …
1. Missing number for $12 + 29 + 37 + \_\_ = 90$: 12 2. Missing number for $18 - 10 = 9 - \_\_$: 1 3. Missing number for $35 + 30 = 45 + \_\_$: 20
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analyze the end behavior of the polynomial function. $f(x) = -x^3 + 8x^…
$\boldsymbol{x \to \infty,\ f(x) \to -\infty}$ $\boldsymbol{x \to -\infty,\ f(x) \to \infty}$
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a pizza box with a lid is made from a 19-inch-by-40-inch piece of cardb…
2.88
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analyze the graph and select all properties that apply to the polynomia…
Maximum: (-6.29,11.10) and (-1.98,30.01) Positive: (-7,-5) and (-4,-1)
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what is the next number in this sequence: 2, 6, 10, 14? select one: a. …
1. b. 18 2. d. 10
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write your answer as an integer or as a positive or negative mixed numb…
### First Section (Integer/Mixed Number): 1. $-18 \div -7 = 2\frac{4}{7}$ 2. $28 \div -4 = -7$ 3. $30 \div 9 = 3\frac{1}{3}$ 4. $-7 \div -6 = 1\frac{1}{6}$ 5. $-80 \div -10 = 8$ 6…
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2. calculate. (1) $\frac{1}{3}+\frac{1}{6}+\frac{1}{8}$ $=$ (2) $\frac{…
(1) $\frac{5}{8}$ (2) $\frac{3}{5}$ (3) $\frac{23}{42}$ (4) $\frac{13}{24}$ (5) $\frac{25}{48}$ (6) $\frac{1}{2}$
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the distance between $-1$ and $7$ on a number line equals $|-1 - 7|$ un…
D. 8 units
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8. graph the function $f(x) = 3 + \\sqrt{x}$.
The graph is a vertical shift up 3 units of the square root parent function, passing through points $(0, 3)$, $(1, 4)$, $(4, 5)$, $(9, 6)$, with a domain of $x \geq 0$ and range o…
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hobbes and the need for government power the only way to erect such a c…
be completely powerful.
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federalists & anti-federalists name: who would say that? read each stat…
1. F 2. A 3. A 4. A 5. F 6. F 7. A 8. F 9. A 10. A 11. F 12. F 13. A 14. F For "Sound Off": One could disagree with Hamilton: The Constitution's creation by the people does not in…
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part 2 of 2 think about the process what should you do first to $y=\\fr…
A. Plot a point at the y-intercept. To graph the line fully: 1. The y-intercept is $b=-1$, so plot the point $(0, -1)$. 2. The slope $m=\frac{1}{5}$, meaning from the y-intercept,…
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question 21 (1 point)amendment 21: repeals amendment _____.○17○18questi…
1. Question 21: 18 2. Question 22: number 3. Question 23: presidential
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use the functions to answer parts a and b. $f(x)=0.75x$ $g(x)=0.09375x^…
## Part a: $f(6)=4.5$, $f(8)=6$, $f(12)=9$ $g(6)=3.375$, $g(8)=6$, $g(12)=13.5$ $h(6)\approx3.815$, $h(8)\approx5.961$, $h(12)\approx14.552$ ## Part b: When $x=11$ (the smallest i…
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explain the difference between the establishment clause and the free ex…
### First Question Answer: - The Establishment Clause forbids government from establishing or endorsing a national religion and limits state-religion entanglement. - The Free Exer…
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nameperioddatetopic 06 – class 04 – exponential growth and decayself-as…
a. $y = 500000(1.15)^t$ b. About 1,156,530 members The function $y=ab^x$ represents exponential growth when $a>0$ and $b>1$.
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question evaluate. express your answer in scientific notation. $2.7 \\t…
$6.97 \times 10^{-1}$
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**#5.) express in simplest radical form: $sqrt{8} \times sqrt{6}$ #6.) …
#5: $4\sqrt{3}$ #6: A) $\frac{4\sqrt{5}}{5}$ #7: b. $(0, 3)$ #8: $5\sqrt{30} - 1$
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2. what basic principle of mercantilism was disproved by adam smith in …
that there was a fixed and limited amount of wealth in the world
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10. $y=\\frac{1}{2}\\cdot2^{x}-4$ growth / decay domain: ________ range…
Growth / Decay: Growth Domain: $(-\infty, \infty)$ Range: $(-4, \infty)$ y-intercept: $\boldsymbol{-\frac{7}{2}}$ (or $-3.5$) Asymptote: $\boldsymbol{y=-4}$
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1. how did the reform act of 1832 change the organization of political …
The Reform Act of 1832 redrew the lines of parliament districts to reflect an industrialized England.
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4. why did adam smith believe that factory workers should be paid highe…
A. Adam Smith knew that higher wages would grow the economy.
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4. what role did adam smith play in moving europe away from mercantilis…
Adam Smith proved that capitalism, not mercantilism, let to the greatest increase in a nation's wealth.
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¿en qué intervalo del dominio la función es creciente? a. $(-\\infty, 4…
DO. $(-\infty, -4)$
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question 13. the table represents some points on the graph of quadratic…
B. All real numbers less than or equal to $\frac{19}{4}$
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considere la función por partes dada.$f(x) = \\begin{cases}-(3x + 7); &…
Las secciones donde la función es decreciente son: 1. $x < -3$ (rama azul del gráfico) 2. $-3 \leq x \leq 0$ (parte izquierda de la rama roja del gráfico) 3. $x > 3$ (rama derecha…
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1-5 lesson quizsolving equations and inequalities by graphing1. sketch …
1. (Graph: Plot $y=-2|x-1|+3$ (V-shaped, vertex at (1,3), slope $\pm2$) and $y=\frac{2}{5}x-\frac{11}{5}$ (line with slope $\frac{2}{5}$, y-intercept $-\frac{11}{5}$); their inter…
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write a rule for $g$. let the graph of $g$ be a translation 2 units dow…
$\log(-x) - 2$
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write a rule for $g$. let the graph of $g$ be a vertical stretch by a f…
$g(x)=3e^{x+6}+3$
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11 country x - universal healthcare system - mixed level of government …
B. Country Y
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country x- universal healthcare system- mixed level of government inter…
C. Country Z
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7. $y=\\frac{1}{2}\\cdot4^{x}$ growth / decay domain: ________ range: _…
Growth / Decay: Growth Domain: $(-\infty, +\infty)$ Range: $(0, +\infty)$ y-intercept: $\frac{1}{2}$ Asymptote: $y=0$
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at what point(s) on the graph of $f(x)=x^3 + 12x^2 + 54x + 14$ is the s…
$(-4, -74)$
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find all the values of x where the tangent line is horizontal. $f(x)=2x…
$x = -7$ and $x = -5$
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52,455×5,555 291,387,525
291,387,525
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1. $\begin{array}{r} square \\ \times 5 \\ hline 10 end{array}$ $xright…
The value in the box is 2, and the result of $5 \enclose{longdiv}{10}$ is 2.
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which of the relationships below represents a function with the same ra…
C
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find the slope of the tangent line to the graph of the given function a…
## Multiple Choice Answer: A. Substitute 2 for x into the derivative of the function and evaluate. ## Tangent Line Results: Slope of the tangent line: $-4$ Equation of the tangent…
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$f(x)=x^{2}+8x+12$ $-7,-4$ $boc = \\underline{\\quad\\quad}$
$[-4, 5]$
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1. $\begin{array}{r} square \\ × 5\\ hline 10 end{array}$ $\boldsymbol{…
2. $4$ 3. $4$ 4. $4$ 5. $2$ 6. $3$ 7. $9$ 8. $4$ 9. $5$ 10. $4$ 11. $3$ 12. $5$
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name: jasean watts date: 02/10/24 bell: unit 4: linear equations homewo…
1. For $y=-\frac{2}{5}x-3$: Line passes through $(0,-3)$ and $(5,-5)$, extended. 2. For $y=\frac{1}{2}x+2$: Line passes through $(0,2)$ and $(2,3)$, extended. 3. For $y=6x-5$: Lin…
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complete the table and then graph the function. $f(x)=2x + 20$ | $x$ | …
Completed table: | $x$ | $f(x)$ | |-----|--------| | $-9$ | $2$ | | $-8$ | $4$ | | $-6$ | $8$ | Graph points to plot: $(-9, 2)$, $(-8, 4)$, $(-6, 8)$; draw a straight line through…
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functions over the start box. use your solution to move t ished! box. s…
3
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consider the following limit statement:$lim_{x \to -1} (5x + 11) = 6$fi…
$\boldsymbol{\delta=0.001}$ (Option: $\boldsymbol{\delta = 0.001}$)
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final milestone | calculus i final milestone calculate $intleft(48sqrt3…
$\frac{144}{5}x^{\frac{5}{3}} + 23x - 21\ln|x| - \frac{5}{x^5} + c$ (matches the first option)
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move at least one of the 3 guide points below to complete the graph of …
1. Keep the blue point at $(0,0)$. 2. Move the red point at $(1,1)$ to $(1, 1.5)$. 3. Move the red point at $(4,2)$ to $(4, 3)$. This will form the correct graph of $y=\frac{3}{2}…
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final milestone consider the function $f(x) = -x^2 - 4x + 5$. use it to…
A. $f(2) = - 7$, $f(-3) = 8$, $f(a - 4) = -a^2 + 4a + 5$
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question 19 for $varepsilon > 0$, find $delta > 0$ necessary to prove $…
$\boldsymbol{\delta = \frac{\varepsilon}{9}}$ (corresponding to the first option)
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find the global maximum and minimum points of the function $f(x)=3x^5 -…
The global minimum is -29 at x = -2. The global maximum is 621 at x = 3.
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write newtons formula used to approximate $sqrt3{7.5}$, a solution of t…
$x_{n+1}=x_n-\frac{x_n^3 - 7.5}{3x_n^2}; x_3\approx 1.957433821$
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let $f(x) = -x^2 - 5$ and $g(x) = 3x + 2$. find and simplify $(g \\circ…
B. $(g \circ f)(x) = -3x^2 - 13$
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find the derivative of $f(x) = -4x^5 - 11\\sin x + \\frac{7}{x^5}$.$\\b…
$f'(x)= -20x^{4}-11\cos x-\frac{35}{x^{6}}$ (the fourth option)
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multiplying powers of 10 steps: 1. count the zeros in the power of 10. …
① $65.7$ ② $1500$ ③ $5260$ ④ $82$ ⑨ $970.8$ ⑩ $6100$ ⑪ $74000$ ⑫ $280.1$ ⑬ $320$ ⑭ $4405$ ⑮ $0.5$ ⑯ $7240$
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questions 1 through 3 refer to the following. \the work accomplished --…
B. Food prices rose as a result of increased demand for grain from coastal port cities.
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graph the equation. 10. $y - 6 = 3(x - 4)$ 11. $y + 1 = 2(x - 5)$ 12. $…
The graph is a straight line passing through points $(0, -3)$ and $(1, 2)$, extending infinitely in both directions.
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question 9 the slope between the points (6, -12), (15, -3) is blank1...…
Question 9: $1$ Question 10: $-\frac{25}{21}$
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given that $f(x)=6x + 7$ and $g(x)=x^3$, find $(f \\circ g)(-2).$ $(f \…
$-41$
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rewrite $f(x) = |2x + 4| + 1$ as a piecewise function. $f(x)=\\begin{ca…
$f(x)=\begin{cases} -2x - 3 & \text{if } x \leq -2 \\ 2x + 5 & \text{if } x > -2 \end{cases}$
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given that $f(x)=3x + 3$ and $g(x)=x^2 - 4x - 5$, find $(g \\circ f)(5)…
247
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q 3 which of the following statements are true about the graph of $f(x)…
B. II and IV only
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q2 when compared to $f(x)=e^x$, how does the graph of $g(x)=3e^{x+2}+4$…
D. Vertical stretch of 3, shifted left 2 units, and shifted up 4 units
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without graphing, determine whether the function represents exponential…
The function represents exponential growth. The y-intercept is $(0, 4)$
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without graphing, determine whether the function represents exponential…
The function represents exponential decay. The y-intercept is 5