微積分
極限、導関数、最適化、関数挙動。
-
evaluate the integral below by interpreting it in terms of areas. in ot…
$2\pi$
-
find the value v of the riemann sum $v = \\sum_{k=1}^{n} f(c_k)\\delta …
164
-
find the value of the summation.\\(\\sum_{k=0}^{11} \\sin(\\pi k) =\\)
0
-
given $g(x) = 5x + 1$, find $g(-2)$. answer attempt 1 out of 2
\( -9 \)
-
what are the vertical and horizontal asymptotes for the function $f(x)=…
vertical asymptote: $x = 1$ horizontal asymptote: $y = 0$
-
solve the system by graphing.\\begin{cases}x - y = 1\\\\y = 3\\end{case…
The solution to the system is \( x = 4,y = 3 \) or the ordered pair \( (4,3) \)
-
write the sum using sigma notation: $4 + 6 + 8 + 10 + \\cdots + 26 = \\…
$A = 12$ $B = 2n + 2$
-
write the sum using sigma notation: $1 + 2 + 3 + 4 + \\cdots + 124 = \\…
$A = 124$ $B = n$
-
find the value of the summation.\\(\\sum_{k=0}^{3} (k^2 + 3) = \\square…
26
-
for what values of a and m does f(x) have a horizontal asymptote at y =…
C. $a=-1, m=1$
-
solve the system by graphing.\\begin{cases}y = 2x - 2\\\\y = -3x + 3\\e…
The solution is \((1,0)\) (the point where the two lines intersect when graphed).
-
activity 3 • distributed practice solve. 1. \\(\\frac{1}{2}+\\frac{1}{4…
1. $\frac{3}{4}$ 2. $\frac{2}{5}$ 3. $\frac{1}{3}$ 4. $\frac{5}{18}$ 5. $\frac{3}{4}$ 6. $15$ 7. $7110$ 8. $918$
-
1. \\(\frac{1}{2} \\cdot \\frac{1}{3}\\) 2. \\(\frac{1}{4} \\cdot \\fra…
1. $\frac{1}{6}$ 2. $\frac{1}{12}$ 3. $\frac{1}{8}$
-
solve the system by graphing. \\begin{cases} y = 2x - 2 \\\\ y = -3x + …
The solution is \((1,0)\)
-
activity 1 find the product by looking at the area model. model (\frac{…
1. $\frac{3}{8}$ 2. $\frac{1}{10}$ 3. $\frac{1}{2}$ 4. $\frac{1}{6}$
-
solve the system by graphing.\\begin{cases}2x + 3y = 6\\\\6x = -9y + 18…
The system of equations has infinitely many solutions, and the two lines coincide (they are the same line \(y =-\frac{2}{3}x + 2\)).
-
(a) what is $limlimits_{x\to -6^{-}} f(x)$? (b) what is $limlimits_{x\t…
To solve these problems, we need the graph of the function \( f(x) \). Since the graph is not provided, we can only explain the general methods to solve each part: ### Part (a): \…
-
cat - culate the height of the cats eyes is $h(x) = 2x + 3$, where $x$ …
- For \( h(5) \): \( 13 \) - For \( h(3) \): \( 9 \) - For \( h(7.5) \): \( 18 \)
-
kanna wrote the function $d(x) = \\frac{1}{2}x$ to determine the wheel …
The wheel distance \( d(x) \) is half of the truck length \( x \), i.e., \( d(x)=\frac{1}{2}x \) implies \( d(x) \) is proportional to \( x \) with a constant of proportionality \…
-
one reform khrushchev instituted was to eliminate the secret police. li…
C. allow political prisoners to be freed.
-
multiplying square roots date simplify. 1) \\(sqrt{5} cdot sqrt{5}\\) \…
Let's solve each problem step by step using the property of square roots: $\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}$ (for $a \geq 0, b \geq 0$) and also handling coefficients. ### 1) $…
-
write an exponential decay function to model the situation. compare the…
The exponential decay function to model the situation is \( f(x) = 52(0.7)^x \). The average rate of change over \( 1 \leq x \leq 4 \) is \(\approx -7.972\). The average rate of c…
-
write an exponential decay function to model the situation. compare the…
$f(x) = 52(0.7)^x$
-
the function $f(x)$ is graphed below. how many points on the graph repr…
1
-
if \\(\\int_{4}^{-10} g(x) dx = -3\\) and \\(\\int_{4}^{6} g(x) dx = 5\…
D. 8
-
whether the function has an inverse function. $f(x) = \\sqrt{x - 4}$, $…
\( f^{-1}(x)=x^{2}+4 \), \( x\geq0 \)
-
when the area in square units of an expanding circle is increasing twic…
\(\frac{1}{\pi}\)
-
determine whether the function has an inverse function. $f(x) = |x - 7|…
Yes, \( f \) does have an inverse. \( f^{-1}(x)=7 - x\), \( x\geq0\)
-
(d) state the domain and range of f. (enter your answers using interval…
To solve for the domain and range of a function \( f \) and its inverse \( f^{-1} \), we use the relationship between a function and its inverse: ### Key Relationship: - The **dom…
-
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)
-
the function $f(x)$ is defined below. what is the end behavior of $f(x)…
as \( x \to -\infty \), \( f(x) \to \infty \) and as \( x \to \infty \), \( f(x) \to -\infty \) (the last option among the choices, which is the one with "as \( x \to -\infty, f(x…
-
the function $f(x)$ is defined below. what is the end behavior of $f(x)…
as \( x \to \infty, y \to -\infty \) and as \( x \to -\infty, y \to -\infty \) (the third option in the list of choices)
-
consider the following function. $f(x) = \\frac{x - 3}{x + 3}$ (a) find…
The graph of \( f^{-1} \) is the reflection of \( f \) in the line \( y = x \). (So the correct option is "The graph of \( f^{-1} \) is the reflection of \( f \) in the line \( y …
-
consider the following function. \\( f(x) = -\\frac{3}{x} \\) \\( \\tex…
\( f^{-1}(x)=-\dfrac{3}{x} \)
-
(b) graph both ( f ) and ( f^{-1} ) on the same set of coordinate axes.…
The graph of \( f^{-1} \) is the reflection of \( f \) in the line \( y = x \). ### Part (d) (Assuming the function \( f \) is a hyperbola - like function, likely \( f(x)=\frac{1}…
-
use the table of values for ( y = f(x) ) to complete a table for ( y = …
| \( x \) | \( f^{-1}(x) \) | |--------|----------------| | -10 | -3 | | -6 | -2 | | -2 | -1 | | 2 | 0 | | 6 | 1 | | 10 | 2 |
-
d rectangles. then, find the total area of the large angles. b. \\(12 \…
First blank: \(10\) Second blank: \(10\) Third blank: \(50\) Fourth blank: \(60\) Area: \(60\) square units
-
12. the function ( f(x)=ln x ) is transformed so that the transformed f…
D. \( g(x)=\ln(x - 5)+3 \) ### Question 13
-
which of the following describes the end behavior for the graph shown h…
2. As \( x \to -\infty \), \( y \to -\infty \) and as \( x \to \infty \), \( y \to \infty \)
-
11. critique reasoning inez graphed ( g(x)=log x + 5 ), as shown. she s…
Inez is incorrect because the function \( g(x)=\log x + 5 \) (for base \( > 1 \)) has a range of all real numbers. As \( x \) increases, \( \log x \) increases without bound (albe…
-
2- opérations dans lensemble des nombres rationnels. a) $\\boldsymbol{\…
a) $\frac{3}{10}$ b) $\frac{2}{15}$ c) $4$ d) $30$
-
first, write an equivalent expression to 856.2 ÷ 0.6 with 6 as the divi…
\(8562\)
-
find the difference. $1\\frac{3}{5}-1\\frac{4}{5}=\\frac{?}{?}$
\(\frac{1}{5}\) (So the numerator is 1 and the denominator is 5)
-
taylor receives the following email from an online clothing store. what…
C) to convince Taylor that he should buy clothing right now
-
a soccer ball is kicked from the ground with an initial upward velocity…
\( h_{\text{max}} = \boxed{400} \) feet ### Part (b)
-
lacronyme pedmas (également appelé pemdas) aide à mémoriser les priorit…
a) $-9$ b) $9$ c) $5$ d) $0$
-
now use the division algorithm to solve the equivalent expression, 8,45…
The result of \( 8456\div7 \) (and also \( 84.56\div0.07 \)) is \( 1208 \). And the long - division boxes are filled as follows: - Quotient: \( 1\), \( 2\), \( 0\), \( 8 \) - Firs…
-
solve 84.56 ÷ 0.07. first, write an equivalent expression to 84.56 ÷ 0.…
\(8456\)
-
the expansive future is our arena, and for our history. we are entering…
The quotation frames westward expansion as a divinely - sanctioned, unstoppable “march” of “human progress”, reflecting the settlers' attitude that their actions were righteous an…
-
9. math on the spot a group of students retake the written portion of a…
### Part 1: Transformation of the Parent Function The parent function is \( f(t)=\log(t) \). Let's analyze the transformations to get \( a(t) = 90-10\log(t + 2) \): 1. **Horizonta…
-
1- convertir les nombres fractionnaires en fractions impropres, sil y e…
a) $-\frac{27}{20}$ b) $\frac{14}{9}$ (ou $1\frac{5}{9}$)
-
heres a graph of a linear function. write the equation that describes t…
$y = 2x - 3$
-
question find the value of ( f(-6) ). answer attempt 3 out of 3 2 submi…
\( - 6 \) (Wait, no, maybe I misread. Wait, maybe the graph at x=-6 is at y = - 6? Wait, let's check again. The x - axis: x=-6 is 6 units left of origin. The y - axis: if the grap…
-
what is the vertex of the quadratic function ( f(x) = (x - 6)(x + 2) )?
$(2, -16)$
-
a) choose the sum that is greater than 5. $4\\frac{5}{8} + \\frac{7}{8}…
\(4\frac{5}{8}+\frac{7}{8}=5\frac{4}{8}\) (or \(5\frac{1}{2}\) after simplifying the fraction \(\frac{4}{8}\) to \(\frac{1}{2}\))
-
which graph shows the solution to the system of linear inequalities? x …
The correct graph is the top one with the overlapping shaded region above the dashed line $y = -\frac{1}{3}x + 2$ and the solid line $y = 2x + 4$ (the upper shaded area in the ima…
-
which ordered pairs are in the solution set of the system of linear ine…
(5, -2), (3, 1), (4, 2)
-
3) is the relation shown in the table below a function? input \t1 \t3 \…
No (the option with "No" as the text, which is the second option in the given choices: the one with the green dot indicating it was previously selected, and the text "No")
-
compare the student text with the source. source: erin blakemore, \four…
No, it is not plagiarized.
-
v = -3x + 5 x | y -1 | 1 | 3 | 4 | (and a coordinate grid is present)
Completed table: | $x$ | $y$ | |-----|-----| | -1 | 8 | | 1 | 2 | | 3 | -4 | | 4 | -7 | The graph is a straight line passing through the points $(-1, 8)$, $(1, 2)$, $(3, -4)$, and…
-
4) how do i find $6\\frac{2}{5}+\\frac{4}{5}$? 4) i can break apart 4/5…
\( 6\frac{2}{5} + \frac{4}{5} = 6\frac{2}{5} + \frac{3}{5} + \frac{1}{5} = 7\frac{1}{5} \) So the first box is \( 7 \), the numerator of the fraction is \( 1 \), and the denominat…
-
fill in the tables and sketch the exponential functions. 4.) \\( y = - …
### Problem 4: \( y = -5(4)^x \) #### Step 1: Determine Growth/Decay, Reflection, Stretch/Compression - **Growth/Decay**: The base \( 4 > 1 \), but there's a negative sign. Howeve…
-
question solve the system of equations graphed on the coordinate axes b…
The solution is $(0, 8)$
-
question given the definitions of f(x) and g(x) below, find the value o…
20
-
question given the definitions of $f(x)$ and $g(x)$ below, find the val…
\( 5 \)
-
use the graph of g to find g(5). g(5) = \\square
\(3.125\) or \(\frac{25}{8}\)
-
use the given conditions to write an equation for the line in point - s…
Point-slope form: $y + 7 = -4(x + 3)$ Slope-intercept form: $y = -4x - 19$
-
y = 2x - 4\ \ | x | y |\ | -2 | |\ | 3 | |\ | 5 | |\ | 6 | |
| $x$ | $y$ | |-----|-----| | -2 | -8 | | 3 | 2 | | 5 | 6 | | 6 | 8 | To plot the line: mark the points $(-2, -8)$, $(3, 2)$, $(5, 6)$, $(6, 8)$ on the coordinate grid, then draw …
-
4) final round! this time, there is just one clue. write your answer as…
\(13\frac{1}{4}\)
-
use the graph to determine a. open intervals on which the function is d…
a. A. The function is decreasing on the interval(s) $(-\infty, \infty)$ b. B. The function is never increasing. c. B. The function is never constant.
-
use the graph to determine a. open intervals on which the function is d…
a. B. The function is never decreasing. b. A. The function is increasing on the interval(s) $(-5, 5)$ c. B. The function is never constant.
-
next round! follow the three clues to find a hidden treasure. write eac…
\( 4\frac{2}{5} \) (So the first box is 4, the numerator box is 2, and the denominator is 5 as given.)
-
c. $y = -2x + 6$ | x | y | | ---- | ---- | | 0 | 6 | | 3 | 0 | | 4 | -2…
A straight line passing through the points $(0, 6)$, $(3, 0)$, and $(4, -2)$ is graphed on the coordinate plane.
-
next round! follow the three clues to find a hidden treasure. write eac…
\( 3\frac{2}{5} + \frac{2}{5} = 3\frac{4}{5} \)
-
epresenta gráficamente la func b) $y = \\frac{1}{2} \\cdot 4^x$
1. Tabla de valores correcta: | $x$ | -2 | -1 | 0 | 1 | 2 | 3 | 4 | |-----|----|----|---|---|---|---|---| | $y$ | $\frac{1}{32}$ | $\frac{1}{8}$ | $\frac{1}{2}$ | 2 | 8 | 32 | 128…
-
give the slope and the y-intercept of the line with the given equation.…
### Slope: A. The slope is $3$ ### Y-intercept: A. The y-intercept is $6$ ### Graph Instructions: Plot the points $(0, 6)$ and $(1, 9)$ (or $(-1, 3)$), then draw a straight line t…
-
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{…
-
unit 5 review score: 33/71 answered: 9/18 question 10 graph the followi…
\((0, -1)\)
-
gráficamente la funci b) $y = \\frac{1}{2} \\cdot 4^x$ | x | -2 | -1 | …
# Explicación: ## Paso 1: Calcular y para x=-2 Sustituir $x=-2$ en la función: $y=\frac{1}{2}\cdot4^{-2}=\frac{1}{2}\cdot\frac{1}{4^2}=\frac{1}{2}\cdot\frac{1}{16}=\frac{1}{32}$ #…
-
3. completa la tabla de valores. representa g a) $y = 2 \\cdot 6^x$ | x…
### Tabla completada: | $X$ | -4 | -3 | -2 | -1 | 0 | 1 | 2 | |-----|----|----|----|----|---|---|---| | $Y$ | $\frac{1}{648}$ | $\frac{1}{108}$ | $\frac{1}{18}$ | $\frac{1}{3}$ | …
-
unit 5 review score: 30/71 answered: 8/18 question 8 score on last try:…
The rocket will be at a height of 63 feet at approximately \(t\approx1.43\) seconds and \(t\approx2.76\) seconds. If we consider the two - decimal - place rounded values, the answ…
-
5×8= 4×9= 7×3= 8×6= 4×3= 6×6= 8×8= 4×5= muestra tu trabajo.
\(5 \times 8 = 40\) \(4 \times 9 = 36\) \(7 \times 3 = 21\) \(8 \times 6 = 48\) \(4 \times 3 = 12\) \(6 \times 6 = 36\) \(8 \times 8 = 64\) \(4 \times 5 = 20\)
-
select the correct answer. the parent cosine function is shifted 5 unit…
B. The midline is $y = 2$
-
fill in the missing number: 2 1 × 4 1 ------ □ □ + 8 4 0 ------ 8 6 1
21
-
question solve for ( x ), rounding to the nearest hundredth. ( 10^x = 7…
$x \approx 1.85$
-
fill in the missing number: 5 0 × 9 6 overline{ 3 0 0} + squaresquaresq…
4500
-
fill in the missing number: 3 0 × 1 2 ------ 6 0 + 3 0 0 ------ □□□
360
-
lauras function is a transformation where the parent function is horizo…
- Left Graph: Becky's function ($f(x) = 3\cos(x - \pi)$) - Right Graph: Laura's transformed function ($y=-\cos(3x)$) - Middle Graph: Neither student's function
-
22. you deposit $1000 in a savings account that earns 5% annual interes…
s: a. The exponential equation is $\boldsymbol{1500 = 1000(1.05)^t}$ (or $y = 1000(1.05)^t$ with $y = 1500$). b. The time $t$ is approximately $\boldsymbol{8.31}$ years.
-
sketch the graph of the function below, including correct signs, x-inte…
x-intercepts: $(-4, 0)$, $(-2, 0)$, $(1, 0)$, $(3, 0)$ y-intercept: $(0, 96)$
-
write a function in any form that would match the graph shown below.
$y = x^3 - 9x^2 + 15x + 50$
-
directions: show work for full credit. evaluate each expression using g…
50 ### Problem 2: $7^2 - 10$
-
write a function in any form that would match the graph shown below.
$y = -3(x+1)(x-2)^2$ (or expanded form $y = -3x^3 + 9x^2 - 12$)
-
solution write a function in any form that would match the graph shown …
$y=\frac{1}{2}(x+1)^2(x-4)$
-
use transformations of ( f(x) = sqrt{x} ) to graph the following functi…
C. <The graph with domain $x\geq-6$, passing through $(-6,-5), (-5,-2), (-2,1)$>
-
write the equation of this line in slope - intercept form. write your a…
$y=\frac{1}{5}x - 5$
-
use transformations of ( f(x)=sqrt4{x} ) to graph the following functio…
(Select the option corresponding to the graph with starting point $(3,1)$, steep upward curve for $x\geq3$; based on standard transformations, this matches the graph that is shift…
-
use transformations of ( f(x)=sqrt{x} ) to graph the following function…
A. <Graph with starting point at (-3,5), increasing curve matching the transformed square root shape>
-
when the area in square units of an expanding circle is increasing twic…
\(\frac{1}{\pi}\)
-
use transformations of ( f(x)=sqrt{x} ) to graph the following function…
C. (The graph starting at (3,2) and curving upward to the right)