Calculus
Limits, derivatives, optimization, and behavior of functions.
- suppose \\(g(x) = f(7 - x)\\) for all \\(x\\), \\(\\lim_{x \\to 7^+} f(…
- calculate the limit \\(\\lim_{x \\to a} \\frac{x^5 - a^5}{x - a}\\) usi…
- the magnitude of the electric field at a point x meters from the midpoi…
- a. evaluate \\(\\lim_{x \\to 1^+} \\sqrt{x-1}\\). b. explain why \\(\\l…
- a. evaluate \\(\\lim_{x \\to 1^+} \\sqrt{x-1}\\). b. explain why \\(\\l…
- let \\(f(x) = \\begin{cases} x^2 + 19, & x < -19 \\\\ \\sqrt{x + 19}, &…
- let \\( f(x) = \\begin{cases} x^2 + 19, & x < -19 \\\\ \\sqrt{x + 19}, …
- find the following limit or state that it does not exist. \\\\lim_{h \\…
- find the following limit or state that it does not exist. \\\\lim_{x \\…
- find the following limit or state that it does not exist. \\\\lim_{x \\…
- find the following limit or state that it does not exist. \\\\lim_{x \\…
- suppose p and q are polynomial functions. if \\(\\lim_{x \\to 0} \\frac…
- how are \\(\\lim_{x \\to a^-} p(x)\\) and \\(\\lim_{x \\to a^+} p(x)\\)…
- assume \\(\\lim_{x \\to 5} f(x) = 14\\), \\(\\lim_{x \\to 5} g(x) = 7\\…
- assume \\(\\lim_{x \\to 5} f(x) = 14\\), \\(\\lim_{x \\to 5} g(x) = 7\\…
- compute the following limit assuming \\(\\lim_{x \\to 2} f(x) = 8\\). s…
- for what values of a does \\(\\lim_{x \\to a} r(x) = r(a)\\) if r is a …
- a. \\(\\frac{d}{dx}(e^x \\cos x)\\)
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find and write the missing numbers to make the equations true. 11. $13 …
11. 15 12. 3 13. 12 14. 40 15. 63; Number story: Lila has 28 stickers, and her friend gives her 35 more. How many stickers does Lila have in total? The matching equation is $28 + …
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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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8. expand the logarithmic expression. $log 10x^{5} = square$
$1 + 5\log x$
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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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country x- universal healthcare system- mixed level of government inter…
C. Country Z
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explain the concept of marginal cost. how does it relate to cost? how i…
1. How does the marginal cost relate to cost? A. Marginal cost refers to the rate of change of cost. 2. How is the marginal cost found? B. Marginal cost is found by taking the der…
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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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find the derivative of $f(x)=\\cot(2x^4 + 10x).$ $\\bigcirc$ $f(x)=-\\c…
$f'(x) = -(8x^3 + 10)\csc^2(2x^4 + 10x)$ (the fourth option)
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52,455×5,555 291,387,525
291,387,525
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find the slope of the tangent line to the graph of the given function a…
$\frac{41}{8}$
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which of the relationships below represents a function with a greater s…
D. The function with the table: $x$: $-4, 0, 4, 8$; $y$: $-13, -5, 3, 11$
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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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$f(x)=x^{2}+8x+12$ $-7,-4$ $boc = \\underline{\\quad\\quad}$
$[-4, 5]$
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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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move at least one of the 3 guide points below to complete the graph of …
1. Move the blue vertex point to $(-2, 0)$ 2. Move the first red point to $(-1, 1)$ 3. Move the second red point to $(2, 2)$ This will complete the correct graph of $y=\sqrt{x+2}$.
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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. Blue shift point: $(0,7)$ 2. First red stretch point: $(1,8.5)$ 3. Second red stretch point: $(4,10)$ When these points are placed, the graph of $y=\frac{3}{2}\sqrt{x}+7$ will …
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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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from the graph below, the slope of the line is , and the y-intercept is…
The slope of the line is $\frac{2}{3}$, and the y-intercept is the point $(0, -1)$
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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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given that $h(x)=x^{3}$, find $(h \\circ h)(-3).$ $(h \\circ h)(-3)=\\s…
$-19683$
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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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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 4.
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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
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question 10 find the inflection point(s) for the function $f(x) = -x^5 …
(3,196)
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4. write the equation of a line perpendicular to $y=-2x+1$ that passes …
4. C. $y = \frac{1}{2}x + 2$ 5. A. $y = -3x - 8$ 6. C. -1/2 7. B. -8/5
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what is the domain of $g(x)=6^{-x}$?(type your answer in interval notat…
$(-\infty, \infty)$
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$f(x)=\\begin{cases} 3x+4 & \\text{if } x<2 \\\\ (x-2)^2+3 & \\text{if …
Not continuous at $x=2$ because $\lim_{x \to 2} f(x)$ does not exist
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question 7 mark this question calculate the average rate of change of $…
B. $\frac{1}{4}$
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question 1 (5 points) ✓ saved listen what is the best definition of \un…
b) the state of including or covering all or a whole collectively or distributively without limit or exception
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question 2 find the derivative of $f(x)=(2x^3+3x-12)^6$. $f(x)=6(2x^3+3…
$f'(x)=6(6x^{2}+3)(2x^{3}+3x-12)^{5}$
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the cost function, $c(x)$, in dollars for producing $x$ units is given …
$32.82$
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graph the following piecewise function, determine its range and evaluat…
$f(4)=7$ (Graph: A line $y=-4x-3$ for all $x<0$ with an open circle at $(0,-3)$, and a line $y=2x-1$ for all $x\geq0$ with a closed circle at $(0,-1)$, passing through $(4,7)$)
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solve for $m$. $\frac{e^{2m}}{e^{6}} = e^{10}$
$m = 8$
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which represents the reflection of $f(x) = \\sqrt{x}$ over the x-axis? …
The first table (with values: x=-1: undefined, x=0:0, x=1:-1, x=4:-2) represents the reflection of $f(x)=\sqrt{x}$ over the x-axis.
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10. for what values of $x$ does the graph of $y = 3x^{5} + 10x^{4}$ hav…
B. $x = -2$ only
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which is the graph of $f(x) = \\sqrt{x}$?
The bottom graph (the second option, starting at the origin and curving upward in the first quadrant) is the graph of $f(x)=\sqrt{x}$.
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10. for what values of $x$ does the graph of $y = 3x^5 + 10x^4$ have a …
B. $x = -2$ only
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9. graph $y=2^x - 5$. how does this graph compare to that of $y=2^x$?
The graph of $y=2^x - 5$ is the graph of $y=2^x$ shifted **vertically downward by 5 units**. Specifically: - The horizontal asymptote of $y=2^x$ (which is $y=0$) moves to $y=-5$ f…
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discuss what you notice about the domain, range, intercepts, and asympt…
- Domain: $(-\infty, \infty)$ - Range: $(3, \infty)$ - Intercepts: y-intercept at $(0, 4)$; no real x-intercept - Asymptote: Horizontal asymptote at $y=3$
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8. graph the function and identify all key characteristics: $f(x) = (x …
Dec. Intervals: $(-\infty, 0), (1.5, 2)$
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what you notice about the domain, range, intercepts, and asymptote of $…
- Domain: All real numbers, or $(-\infty, \infty)$ - Range: All real numbers greater than -5, or $(-5, \infty)$ - Intercepts: x-intercept at $(\log_2 5, 0)$, y-intercept at $(0, -…
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9. write in slope intercept form $5x - 3y = -9$ a $y=(3/5)x + 3$ b $y=(…
9. B. $y = (5/3)x + 3$ 10. A. A 11. A. $y=3x+2$
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given the function $f(x)=2x^2 - 3x + 1$, complete the table of values f…
| $x$ | $f(x)$ | |-----|--------| | $-2$ | $15$ | | $-1$ | $6$ | | $0$ | $1$ | | $1$ | $0$ | | $2$ | $3$ |
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5. find the slope. a (-0,-3) b 3/2 c none of the above d -3/2 6. what t…
5. B. 3/2 6. C. Negative 7. B. -20/9 8. A. 2
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(04.04 lc) read the scenario and determine the type of action. ils ont …
Series of completed events
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question 5 what is the equation of the following line? be sure to scrol…
Question 5: E. $y = -\frac{1}{3}x$ Question 6: B. $y = \frac{3}{2}x$
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forms of quadratics tell whether the quadratic function is in standard …
1. Standard form 2. Vertex form 3. Vertex form 4. Standard form 5. $(7, -1)$ 6. $(-2, -5)$ 7. $(3, 0)$ 8. $(2, 4)$ 9. $(-1, -3)$ 10. $(-4, 0)$ 11. $(5, 1)$ 12. $(-6, 10)$ 13. $(4,…
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question 3 what is the equation of the following line? be sure to scrol…
Question 3: D. $y=\frac{2}{7}x$ Question 4: C. $y=-\frac{3}{4}x$
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8/9 what did jefferson insist on instead of hosting showy and expensive…
Meeting personally with members of Congress and foreign leaders for dinner and conversation
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7/9 what did jefferson do to reduce the size of the federal judiciary? …
He decreased the number of federal judges
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6/9 what did jefferson continue to support during his presidency? the p…
The power of the states