微積分
極限、導関数、最適化、関数挙動。
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exercises 1.2 the definite integral score: 140/170 answered: 14/17 ques…
6.7
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1.3) select three ways that the commerce clause has been used to extend…
### 1.3 - It allows Congress to regulate state legislation that might have a negative impact on commerce within a single state. - The Commerce Clause gives Congress nearly unlimit…
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3 finish the algorithm for 612 - 235
377
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sketch a graph of $f(x)=\\begin{cases}5 & \\text{if } x\\leq -2 \\\\ -2…
The graph consists of: - A horizontal line \( y = 5 \) for \( x \leq -2 \) (closed dot at \( (-2, 5) \)). - A line segment \( y = -2x + 1 \) for \( -2 < x \leq 1 \) (open dot at \…
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given the function: $f(x) = \\begin{cases} 8x - 6 & x < 0 \\\\ 8x - 12 …
\( f(-1) = -14 \) \( f(0) = -12 \) \( f(2) = 4 \)
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chapter 1 quiz (1.1,1.2, 1.4, 1.5, 1.7) 14 points possible answered: 2/…
\( 6x + 3h + 1 \)
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exercises 1.2 the definite integral score: 130/170 answered: 13/17 ques…
$0$
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exercises 1.2 the definite integral score: 120/170 answered: 12/17 ques…
$-\frac{8}{3}$
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evaluate the integral below by interpreting it in terms of areas in the…
$-1$
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exercises 1.2 the definite integral score: 100/170 answered: 10/17 ques…
$a=10$ and $b=11$
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given the function graphed below, evaluate the definite integrals. \\(\…
$\int_{0}^{1} f(x) dx = 2$ $\int_{1}^{8} f(x) dx = -10$
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exercises 1.2 the definite integral score: 80/170 answered: 8/17 questi…
13
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match the functions: $y = |x|$, $y = \\frac{1}{x}$, $y = \\frac{1}{x^2}…
s: a. \(y = |x|\) b. \(y=x^{3}\) c. \(y = x^{2}\) d. \(y=\frac{1}{x^{2}}\)
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evaluate the integral below by interpreting it in terms of areas in the…
$0$
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suppose $f(x) = -x^2 - 3x + 3$. compute the following: a.) $f(-5) + f(5…
\( -44 \) ### Part B: Compute \( f(-5) - f(5) \)
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exercises 1.2 the definite integral score: 40/170 answered: 4/17 questi…
$18\pi$
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homework assignment 1.7: inverse functions score: 12.5/15 answered: 13/…
\(-\frac{27}{5}\) (or - 5.4)
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evaluate. $50 + 50 \\div 5^2$
52
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homework assignment 1.7: inverse functions score: 11.5/15 answered: 12/…
\( f^{-1}(x)=\frac{2x - 4}{6x - 1} \)
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exercises 1.2 the definite integral score: 20/170 answered: 2/17 questi…
$a = 4$, $b = 5$, $f(x) = 2x^4 - 5x^5$
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answer the following true or false. if $f(x)$ is continuous with $c > 0…
False
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homework assignment 1.7: inverse functions score: 9.5/15 answered: 10/1…
\( f^{-1}(x)=\frac{x^{2}-10x + 28}{6} \) (or \( \frac{x^{2}}{6}-\frac{5x}{3}+\frac{14}{3} \)) with \( x\geq5 \)
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homework assignment 1.7: inverse functions score: 8.5/15 answered: 9/15…
\( (x - 8)^3 \)
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let $f(x) = \\frac{1}{x + 3}$ $f^{-1}(x) = $
\( \frac{1}{x} - 3 \) (or \( \frac{1 - 3x}{x} \))
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lets find \\(\\frac{2}{3} - \\frac{1}{4}\\). first write the subtractio…
$\frac{2}{3} - \frac{1}{4} = \frac{8}{12} - \frac{3}{12} = \frac{5}{12}$
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lets find \\(\\frac{2}{3} + \\frac{1}{5}\\). first write the addition w…
$\frac{2}{3} + \frac{1}{5} = \frac{10}{15} + \frac{3}{15} = \frac{13}{15}$
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use the aleks calculator to approximate \\(\\sqrt{115.3}\\). round your…
10.74
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use the aleks calculator to approximate \\(\\sqrt{110}\\). round your a…
10.49
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6 × 0.43 =
\(2.58\)
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graph the following functions on the same axes. (a) ( f(x) = 4^x ) (b) …
1. Correct graph: A. 2. For positive constant $c$: - The graph of $y=4^{x+c}$ is the graph of $f(x)=4^x$ shifted horizontally to the left by $c$ units. - The graph of $y=4^{x-c}$ …
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3 × 0.90 = _
2.7
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if f(x)=a^x and f(3) = 64, find f(2). assume a > 0.
16
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what was the significance of mcculloch v. maryland (1819)? it limited t…
B. It confirmed the supremacy of federal law over state law.
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numbers by decimals t 2. $3 \\times 0.045 =$ 4. $1 \\times 0.028 =$ 6. …
\( 0.135 \) ### Problem 4: \( 1 \times 0.028 \)
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graph the equation on paper, and then choose the correct graph. y = 4^x…
C. <The graph that passes through (0,1), rises from left to right, and approaches the x-axis on the left>
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without graphing, complete the following for the function ( k(x) = 3(2^…
### (a) The graph is entirely above the x-axis, rises from left to right, and increases more steeply than the graph of $y=2^x$. ### (b) - For first coordinate 0: 3 - For first coo…
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6 × 0.053 =
\(0.318\)
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write the following logarithm in terms of the natural logarithm. then u…
$\log_2 57 = \frac{\ln 57}{\ln 2}\approx5.8332$
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without graphing, complete the following for the function k(x)=3(2^x). …
(a) The graph is entirely above the x-axis and rises from left to right, equally steeply than the graph of $y=2^x$. (b) For $x=0$, the second coordinate is 3; for $x=1$, the secon…
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use the hints on this page to help you answer the questions. 1 which st…
D. School authorities should not censor school yearbooks because it limits students’ rights and creativity. ### Question 2
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multiply. \\begin{array}{r} 70.6 \\\\ \\times\\ 53.9 \\\\ \\hline \\end…
$3805.34$
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without graphing, complete the following for the function k(x)=3(2^x). …
(a) The graph is entirely above the x-axis and, from left to right, increases more steeply than the graph of $y=2^x$. (b) For x=0: $(0, 3)$; For x=1: $(1, 6)$
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multiply. \\begin{array}{r} 8.95 \\\\ \\times\\ 50.7 \\\\ \\hline \\end…
$453.765$
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multiply. \\begin{array}{r} 8.49 \\\\ \\times\\ 0.63 \\\\ \\hline \\end…
$5.3487$
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without graphing, describe the shape of the graph of the function. find…
$f(0)=1$, $f(1)=2.6$ The graph is an exponential growth curve that passes through the points $(0,1)$ and $(1,2.6)$, increasing rapidly as $x$ increases, approaching $0$ as $x$ app…
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without graphing, describe the shape of the graph of the function. find…
The graph exponentially grows. Second coordinate for $x=0$: $1$ Second coordinate for $x=1$: $\approx2.639$
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graph the following function on the axes provided. $f(x) = \\begin{case…
To graph the piecewise function: 1. **For \( \boldsymbol{x < -4} \) (function \( -4x - 22 \))**: - Slope \( -4 \), open circle at \( (-4, -6) \) (since \( x < -4 \)), pass through…
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write the following logarithm in terms of the natural logarithm. then u…
$\log_5 20\approx 1.8607$ (and in terms of natural logarithms, $\log_5 20 = \frac{\ln 20}{\ln 5}$)
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use the drawing tool(s) to form the correct answer on the provided grap…
The graph is a V-shaped absolute value graph with vertex at $(3,1)$, passing through $(0,4)$ and $(6,4)$, formed by two rays extending from the vertex.
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let $f(x) = 5x + 3$ $f^{-1}(x) = $ question help: video written example…
\( \frac{x - 3}{5} \)
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what is $2\\frac{4}{6}+5\\frac{3}{6}$? $7\\frac{1}{6}$ $7\\frac{7}{12}$…
\(8\frac{1}{6}\) (corresponding to the option \(8\frac{1}{6}\))
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evaluate the expression. -6 × (-3.2 - 0.4 + 1.4) = submit
13.2
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homework assignment 1.7: inverse functions score: 4/15 answered: 4/15 q…
(a) \( f^{-1}(x)=\boldsymbol{\frac{x + 6}{8}}\) (or \( \frac{1}{8}x+\frac{3}{4}\)) (b) \( y = \boldsymbol{x}\)
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solve the following equation. $5^{5x - 4} = 10$ $x = \\square$ (type an…
$x = \frac{\log_{5}10 + 4}{5}$ (or equivalent forms like $\frac{\ln 10 + 4\ln 5}{5\ln 5}$)
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solve the following equation. $5^{5x - 4} = 10$ $x = \\square$ (type an…
\(\frac{\log_{5}(10)+4}{5}\) (or equivalent forms like \(\frac{\ln(10)+4\ln(5)}{5\ln(5)}\) or \(\frac{\ln(6250)}{5\ln(5)}\))
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what is $\frac{3}{8} div \frac{5}{9}$? $\frac{15}{40}$ $\frac{27}{40}$ …
\(\frac{27}{40}\) (corresponding to the option with \(\frac{27}{40}\))
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without graphing, describe the shape of the graph of the function. find…
- The graph is an exponential growth curve: it approaches 0 as $x\to-\infty$, passes through $(0,1)$, and increases rapidly as $x$ increases. - $f(0)=1$ - $f(1)=2.9$
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use the graph below to fill in the missing values. $f(0) = \\square$ $f…
\( f(0) = \boldsymbol{3} \) \( f(x) = 0 \), \( x = \boldsymbol{1} \) \( f^{-1}(0) = \boldsymbol{1} \) (Wait, no, wait, I think I made a mistake here. Wait, let's re-examine. Wait,…
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without graphing, describe the shape of the graph of the function. find…
The graph is an increasing exponential growth curve, always positive, approaching 0 as $x \to -\infty$, rising as $x$ increases, passing through the points $(0, 1)$ and $(1, 2.9)$…
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homework assignment 1.7: inverse functions score: 0/15 answered: 0/15 q…
(a): \(6\)
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the ancient greek concept of “mimesis,” a term used in the works of pla…
A. One of the earliest appearances of mimesis’s root word, mimos, can be found in an ancient Greek tragedy in reference to dramatic impersonation, and the mim - root came to be ge…
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assume $\\log_{b}x = 0.34$, $\\log_{b}y = 0.52$, and $\\log_{b}z = 0.83…
-0.4
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write \\(\\frac{71}{200}\\) as a decimal number.
0.355
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if \\(\\log_{b}x = 0.38\\) and \\(\\log_{b}z = 0.89\\), evaluate the fo…
1.27
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write \\(\frac{9}{20}\\) as a decimal number.
\(0.45\)
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slope and rate of change each of the line segments in the word math are…
7. Line 1 = Undefined 8. Line 2 = Negative 9. Line 3 = Positive 10. Line 4 = Undefined 11. Line 5 = Positive 12. Line 6 = Negative 13. Line 7 = Zero 14. Line 8 = Zero 15. Line 9 =…
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independent practice 1 describe one example of violence that broke out …
Example: 1936 - 1939 Arab Revolt. Cause: Jewish immigration/land purchases threatened Arab interests. British response: Appointed Peel Commission (recommended partition) and used …
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is the number -9·π rational or irrational? rational irrational submit
irrational
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is the number 7 + −3 rational or irrational? rational irrational
rational
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y = -\\frac{4}{3}x - 6\ y = \\frac{4}{3}x + 2
El punto de intersección es \( (-3,-2) \)
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5. solve: 3 • 5 + 12 - 1 • 2²
23
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23) a function is shown. $f(x) = |x - 7| - 11$ what is the range of the…
\(\{y:-11 < y\}\)
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f(x) = \\begin{cases} -\\frac{5}{2}x + 6 & \\text{for} & x \\leq 2 \\\\…
To plot the closed circles for the piecewise function \( f(x) \), we need to find the points where the function has a closed circle (i.e., where the domain includes the endpoint).…
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10. determine whether each graph represents the graph of a function. if…
To determine if a graph represents a function, we use the **vertical line test**: a graph is a function if no vertical line intersects it more than once. To determine if a functio…
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16) three key features of a linear function are described as shown. - t…
\( f(x)=\frac{3}{4}x + 3 \) ### Question 17
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12. $y = 3x - 10$ $y = 5x - 14$
The solution to the system of equations is \( (2, -4) \)
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read the passage and then answer the question. construction on florence…
B. asked
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suppose that the functions r and s are defined for all real numbers x a…
$(r+s)(x) = 2x^2 + x + 1$ $(r\cdot s)(x) = 2x^3 + 2x^2$ $(r-s)(-3) = -20$
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select the text from the paragraph that best helps you understand that …
- "Over a hundred years later, however, the structure remained unfinished, with an enormous hole in the roof." - "The main factor stalling progress was the fact that no one knew h…
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use the rule for function $f$ to draw its graph. $f(x)=\\begin{cases} 2…
The graph consists of three parts: a horizontal segment \( y = 2 \) from \( (-5, 2) \) (closed) to \( (-2, 2) \) (open), a horizontal segment \( y = 6 \) from \( (-2, 6) \) (close…
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problem 1 what is $5 \\cdot (-7)$? you can think of 5 groups of $-7$ as…
$-35$
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problem 1 select the number line that represents $5 \\cdot (-7)$. you c…
The bottom number line (with 5 leftward arrows each labeled $-7$, starting at 0)
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a small ball is dropped from a tall building. which equation could repr…
B. \(h = 100 - 16t^2\) (or C if B and C are the same, but based on the free - fall formula, this is the correct form)
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the graph of $y = -(x - 4)(x + 2)$ is shown in the $xy$-plane. which of…
A. \( x \)-intercept(s)
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at a gas station, the price of gas is 4 dollars per gallon. the graph b…
4
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8. the reciprocal of 1 is 1 and the reciprocal of -1 is -1. thus, the p…
The graph of \(g(x)=\frac{1}{x + 3}\) has a vertical asymptote at \(x=-3\), a horizontal asymptote at \(y = 0\), passes through \((-2,1)\) and \((-4,-1)\). The right - hand branch…
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read carefully and choose the name of the student who made the correct …
Alejandro ### For the justification part:
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7. sketch the graph of the function $f(x) = |x|$.
The graph of \(f(x)=\vert x\vert\) is a V - shaped graph with vertex at \((0,0)\), the right - hand branch (for \(x\geq0\)) is the line \(y = x\) and the left - hand branch (for \…
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diego is painting the walls of his house. he paints 8 square meters eve…
Horizontal distance (bottom box): 3 Vertical distance (top box): 24 Slope of the line: 8
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details lesson 7.2 - log vs exponent conversions completed notes (comin…
$\frac{1}{125}$
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7. target value: 29 $12\\times2^2 - 18.4\\div0.6$ 8. target value: 23 $…
1. For expression $12 \times 2^2 - 18.4 + 0.6$: $30.2$ (does not match target 29) 2. For expression $5^2 - 0.2 \times 8 + 12 \times \frac{1}{2}$: $29.4$ (does not match target 23)…
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details lesson 7.2 - log vs exponent conversions completed notes (comin…
s: a) \(\log_{2}\frac{1}{4}=-2\) b) \(\log420 = x\) (or \(\log_{10}420=x\)) c) \(\ln x = 5\)
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10. 4.67 ÷ 0.001 =
4670
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express each equation in logarithmic form. (a) $e^x = 7$ is equivalent …
(a) \(\ln(7)=x\) (or \(x = \ln(7)\)) (b) \(\ln(x)=8\) (or \(8=\ln(x)\))
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lesson 7.2 - log vs exponent conversions completed notes (coming soon) …
a) $4^{-2}=\frac{1}{16}$ b) $10^x = 338$ c) $e^4 = x$
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2) $y = -x + 2$
The line $y=-x+2$ is graphed by plotting the points $(0, 2)$, $(2, 0)$, and $(1, 1)$, then drawing a straight line passing through all three points.
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rewrite the following in exponential form: a) \\(\\log_{4}\\left(\\frac…
\(4^{-1}=\frac{1}{4}\) ### Part (b)
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7.1 hw - guess the exponent score: 5.67/12 answered: 6/12 question 7 ev…
\(\frac{1}{2}\)
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find the exact value of the following logarithmic expression. \\(\\log_…
11
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1. find the equation of the line that passes through the point (5, -2) …
The equation of the line is \( y=-\frac{1}{3}x-\frac{1}{3} \) (or \( x + 3y=-1 \))