微積分
極限、導関数、最適化、関数挙動。
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chapter 1post testread each question carefully and choose the best answ…
1. C. allowing for the formation of large corporations 2. H. Protests by farmers and the growth of income disparities between rich and poor led to the formation of an influential …
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question 2 (1 point)determine the symmetry and domain of the polynomial…
Domain: All Real Numbers Symmetry: None
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given the polynomial function, determine the symmetry and positive inte…
Positive: $(-2.88, -0.85) \cup (0.85, 2.88)$ Symmetry: Even
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question the graph of a function is shown below. what is true about the…
it is increasing and non-linear
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the graph of a function is shown below. what is true about the function…
it is increasing and linear
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apply it use what you learned to solve these problems. 5 use the graph …
- Segment A: The function increases at an increasing rate. - Segment B: The function stays constant. - Segment C: The function decreases at a constant rate. - Segment D: The funct…
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2-75. if $g(x)=x^2 - 5$, find the value(s) of $x$ so that: a. $g(x)=20$…
a. $x=5$ and $x=-5$ b. $x=\sqrt{11}$ and $x=-\sqrt{11}$
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use finite approximations to estimate the area under the graph of the f…
a. $\boldsymbol{0}$ b. $\boldsymbol{20.25}$ c. $\boldsymbol{54}$ d. $\boldsymbol{47.25}$
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timed problem score: 5/10 $\frac{d}{dx}(x^{-5})$ answer $-4x^{-4}$ $-5x…
B. $-5x^{-6}$
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timed problem score: 4/10 $int 6x^{5} dx$ answer $30x^{4}+c$ $x^{6}+c$ …
$x^6 + C$ (Option B)
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timed problem score: 3/10 $int 2x^{2} dx$ answer $\frac{2}{3}x^{3}+c$ $…
$\frac{2}{3}x^3 + C$ (Option 1: $\frac{2}{3}x^3 + C$)
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score: 0/10 $\frac{d}{dx}(x^{-3})$ answer $-\frac{1}{4}x^{-4}$ $-3x^{-2…
$-3x^{-4}$
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calculate the integral and write your answer in simplest form. $int \fr…
$\frac{1}{2}x^{\frac{8}{3}} + C$ (or $\frac{1}{2}x^2\sqrt[3]{x^2} + C$)
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10. compute the modulus and argument of each complex number. (4 points)…
a. Modulus: $5$, Argument: $-\frac{\pi}{2}$ (or $\frac{3\pi}{2}$) b. Modulus: $\sqrt{10}$, Argument: $\frac{5\pi}{7}$
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b. identify, graph, and state the symmetries for each polar equation. w…
a. Rose curve with 5 petals; Symmetric with respect to the polar axis; Scale: 1 unit per grid ring. b. Circle; Symmetric with respect to the polar axis; Scale: 0.5 units per grid …
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a graph of a system of two equations is shown. what is the solution of …
$(-3, -2)$
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here is a system of equations.$\begin{cases} y=x-6 \\ y=x-4 end{cases}$…
No solution
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the effects of pontiacs war were limited to the new england region. tru…
False
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what was the importance of jacksonian democracy? ○ it led to the breaki…
A. It led to the breaking of social barriers and institutions.
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find a and b such that f is differentiable everywhere.$f(x)=\begin{case…
$a = 0$ $b = 5$
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ain, range, and evaluate exponential function z.1 domain and range of e…
$\{y \mid y > 0\}$
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what is the slope for the function with the larger slope? mark all that…
B. $\frac{7}{2}$
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omain, range, and evaluate exponential function what is the domain of t…
all real numbers
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what is the domain of this exponential function? { x | x < -6 } all rea…
all real numbers
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domain, range, and evaluate exponential function what is the range of t…
{y | y < -9}
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what is the range of this exponential function?{y | y ≤ -9}all real num…
$\{y \mid y > -9\}$
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the polynomial function $g$ is defined by $g(x) = -4x^4 - 9x^3 + 2x^2 +…
$(x, g(x)) = (-0.67, -0.73)$ and $(x, g(x)) = (1.00, -6.00)$
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find the derivative of the function. $f(t) = 8t^{2/3} - 7t^{1/3} + 1$ $…
$\frac{16}{3}t^{-1/3} - \frac{7}{3}t^{-2/3}$ (or equivalently $\frac{16}{3t^{1/3}} - \frac{7}{3t^{2/3}}$)
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consider the following function. (if an answer does not exist, enter dn…
Derivative from the left at $x=7$: $-1$ Derivative from the right at $x=7$: $1$ Is the function differentiable at $x=7$? $\text{No}$
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express the function graphed on the axes below as a piecewise function.…
$$ f(x) = \begin{cases} \dfrac{4}{3}x + 4 & \text{for } -6 \leq x < 0 \\\\ -2x + 4 & \text{for } 0 < x < 2 \end{cases} $$
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3: domain, range, and evaluate exponential function z.2 evaluate expone…
6.24
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z.2 evaluate exponential functions lwe use the following function rule …
10.37
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express the function graphed on the axes below as a piecewise function.…
$$ f(x) = \begin{cases} \boldsymbol{\frac{3}{2}x + 7} & \text{for } \boldsymbol{-6 \leq x < -2} \\ \boldsymbol{-\frac{3}{2}x + 1} & \text{for } \boldsymbol{-2 < x < 2} \end{cases}…
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domain, range, and evaluate exponential function ixl - domain and range…
390.12
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2 > ★ z.2 evaluate exponential functions lwe use the following function…
-3.83
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w2q3: domain, range, and evaluate exponential function my ixl learning …
-5
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3: domain, range, and evaluate exponential function ixl - domain and ra…
-2.25
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use the properties of logarithms to expand $log(yx^{9}).$ each logarith…
$\log(y) + 9\log(x)$
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z.2 evaluate exponential functions lwe use the following function rule …
-1.97
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fill in the missing values to make the equations true.$log_{8}9 - log_{…
1. $\frac{9}{11}$ 2. $3$ 3. $\frac{1}{9}$
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2q3: domain, range, and evaluate exponential function ixl - domain and …
1
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q3: domain, range, and evaluate exponential function ixl - domain and r…
23.52
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z.2 evaluate exponential functions lwe use the following function rule …
-64
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z.2 evaluate exponential functions lwe use the following function rule …
25
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zq3: domain, range, and evaluate exponential function ixl - domain and …
-23
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w2q3: domain, range, and evaluate exponential function my ixl learni > …
$-57$
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w2q3: domain, range, and evaluate exponential function ixl - domain and…
6
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use the following function rule to find $f(1)$. $f(x) = 9(7)^x + 8$ $f(…
71
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z.2 evaluate exponential functions lwe use the following function rule …
$-9$
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z.2 evaluate exponential functions lwe use the following function rule …
54
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z.2 evaluate exponential functions lwe use the following function rule …
442
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z.2 evaluate exponential functions lwe use the following function rule …
3075
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z.2 evaluate exponential functions lwe learn with an exan use the follo…
249
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evaluate each expression. (a) $log_{6}6 = square$ (b) $log_{4}\\frac{1}…
(a) $1$ (b) $-3$
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which statement best describes shah mohammad reza pahlavi?he instituted…
He instituted education and economic reforms, but limited civil liberties.
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5. $log_{3}(x - 2) + log_{3}(x + 4) = 2$ $log_{3} x - 2(x + 4) = 2$
$x = -1 + 3\sqrt{2}$
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multiple select question select all that apply which of the following a…
- using peer teaching and encouraging children to practice their skills - focusing lessons on the upper limit of a child's zone of proximal development to teach advanced cognitive…
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problem 7 solve this system of equations. $y = -4x + 2$ $y = 3x - 5$ us…
$x=1$, $y=-2$ (or the ordered pair $(1, -2)$)
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20. $g(7)-15$21. $-4-h(-13)$22. $f(-1)+g(-2)$23. given $f(x)=5-3x$, if …
20. $69$ 21. $36$ 22. $-9$ 23. $x=8$ 24. $x=-6$ 25. $f(-6)=-8$ 26. $f(0)=-2$ 27. $x=-3$ 28. $x=9$
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9. find the value of $h$ at each given input. a. $h(-6) =$ b. $h(0) =$ …
a. $h(-6) = -10$ b. $h(0) = 10$ c. $h(2) = 10$ d. $h(7) = 10$ e. $h(0)+2h(10) = 30$
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13. find a formula for a cubic function $f$ if $f(1) = 6$ and $f(-1) = …
$f(x)=-3x^3+3x^2+6x$ (or factored form $f(x)=-3x(x+1)(x-2)$)
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let $f(x) = 5x + 3$ and $g(x) = x^2 - x + 2$. perform the function oper…
$f(x)+g(x)=x^2 + 4x + 5$ Domain: All real numbers (or $(-\infty, \infty)$)
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let $g(x) = -4x$ and $h(x) = x^2 + 5$. find $(g \\circ h)(0)$. $(g \\ci…
$-20$
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let $f(x) = -5x - 1$ and $g(x) = x^2 - 1$. find $(f \\circ g)(-2)$. the…
$-16$
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let $f(x)=2x^2 + x - 23$ and $g(x)=x - 1$. perform the function operati…
$(f+g)(x) = 2x^2 + 2x - 24$ Domain: All real numbers, or $(-\infty, \infty)$
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let $f(x) = 5 - x$ and $g(x) = \\frac{1}{x}$. perform the function oper…
$\frac{f}{g}(x) = 5x - x^2$ Domain: All real numbers except $x=0$, or in interval notation $(-\infty, 0) \cup (0, \infty)$
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find the linear function with the following properties.$f(0) = 6$slope …
$f(x) = -9x + 6$
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let $f(x)=4 - x$ and $g(x)=\\frac{5}{x}$. perform the function operatio…
$(g-f)(x) = x - 4 + \frac{5}{x}$ Domain: All real numbers except $x=0$ (or in interval notation: $(-\infty,0) \cup (0,\infty)$)
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consider the following function. $q(x) = 5x - \\frac{(3 + 5x)}{6}$ step…
Two points on the line are $\boldsymbol{(0, -\frac{1}{2})}$ and $\boldsymbol{(6, \frac{49}{2})}$ (other valid points are also acceptable, e.g., $(1, \frac{11}{3})$)
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11-12 find a formula for the quadratic function shown. 11. 12. (4, 2)
$f(x)=2(x-3)^2$ (or expanded form: $f(x)=2x^2-12x+18$)
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7. is the graph a piecewise function? why or why not? rubric
Yes, this graph represents a piecewise function. It is composed of two distinct sub-functions that apply to non-overlapping intervals of the $x$-domain, and it satisfies the defin…
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7. function $g$ is defined by the equation $g(x) = |x|$. function $r$ i…
Both graphs make a **V-shape**. Graph $R$ is shifted $\boldsymbol{2}$ units **upward**.
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question 9 (1 point)why did king george iii issue the royal proclamatio…
To limit wars with Native Americans, To make it easier to collect taxes
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13 $\frac{9}{8} div \frac{3}{2} =$
$\frac{3}{4}$
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10 $\frac{4}{7} div \frac{10}{5} =$
$\frac{2}{7}$
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$\\frac{3}{2} \\div \\frac{8}{3} =$
$\frac{9}{16}$
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8 $\frac{1}{4} div \frac{4}{2} =$
$\frac{1}{8}$
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7 $\frac{1}{5} div \frac{6}{3} =$
$\frac{1}{10}$
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6 $\frac{1}{6} div \frac{3}{3} =$
$\frac{1}{6}$
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5 2/2 ÷ 9/6 =
$\frac{2}{3}$
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4 $\frac{6}{9} div \frac{5}{6} =$
$\frac{4}{5}$
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part b: written response show all work for full marks. 1. if $f(x)=3x^{…
$f'(x)=6x-2$
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possible points 25 identify the transformation and vertex of the functi…
The transformation of $f(x)$ to $g(x)$ is a horizontal shift 4 units left, a vertical shift 3 units down, and a vertical stretch by a factor of 6 with reflection over the x-axis. …
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powers of 10 directions: solve each of the following. $35 \\times 100 =…
$35 \times 100 = 3500$ $72 \div 100 = 0.72$ $12 \div 1000 = 0.012$ $25 \times 10^3 = 25000$ $32 \times 10^2 = 3200$ $4 \times 10^4 = 40000$ $871 \times 10 = 8710$ $67 \times 10000…
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find the equation of the exponential function. | $x$ | $f(x)$ || ---- |…
$f(x) = 0.1 \cdot 3^x$
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2 look at the multiplication below. what are the factors, partial produ…
factors: 215, 3 partial products: 15, 30, 600 product: 645
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write the equation of the line in fully simplified slope-intercept form.
$y=x+1$
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7. if $h(x)=f(x)^{2}-g(x)^{2}$, $f(x)=-g(x)$, and $g(x)=f(x)$, then $h(…
B. $-4f(x)g(x)$
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3. | $x$ | $y=-x-3$ | $y$ | | ---- | ---- | ---- | | $4$ | $y=-1\\cdot4…
The completed table values for $y$ are: - When $x=4$, $y=-7$ - When $x=-1$, $y=-2$ - When $x=-6$, $y=3$ - When $x=0$, $y=-3$
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finding the slope from points score: 1/2 penalty: none question what is…
$5$
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find the equation of the exponential function. | $x$ | $f(x)$ | | ---- …
$f(x)=2^x$
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answer attempt 1 out of 2 $f(x)=\\begin{cases} \\boxed{\\phantom{0000}}…
$$f(x) = \begin{cases} 4 & \text{for } x<1 \\ x+5 & \text{for } x>1 \end{cases}$$
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find the equation of the exponential function. $x$ $f(x)$ 0 1 1 $1\\cdo…
$f(x) = 2^x$ (or $f(x)=1\cdot2^x$)
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1. the graph of an absolute value function is shown. identify the domai…
Domain: $\boldsymbol{-5 \leq x \leq 5}$ Range: $\boldsymbol{2 \leq y \leq 8}$
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$(10 - 6 + 8 div 2) \times 3$ $7 div (4 \times 2 + 9 - 10)$
24, 1
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1 think about what you know about multiplication. fill in each box. use…
| Word | In My Own Words | Example | |------|-----------------|---------| | partial product | A piece of the total product | When calculating $23 \times 4$, the partial products a…
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$(10 - 6 + 8 div 2) \times 3$
24
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use transformations of $f(x)=x^2$ to graph the following function.$g(x)…
The graph of $g(x)=4(x+1)^2-2$ is a parabola with vertex at $(-1, -2)$, vertically stretched by a factor of 4, shifted left 1 unit and down 2 units from the base parabola $f(x)=x^…
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the main, or central, idea of the passage is encouraging cities to beco…
It explains how sprawl discourages the use of public transit.
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read the passage. american transit blues compared to europeans, america…
Encouraging cities to become denser would likely result in increased public transit use in America.