微積分
極限、導數、最優化與函數性質。
-
find \\(\\int\\left( \\dfrac{7}{x^6} + 6x + 4 \ ight) dx\\) \\(\\boxed{…
$-\frac{7}{5x^5} + 3x^2 + 4x$
-
fill in the equation for this function. y = ?(x - )^3 +
\( y = -2(x - 3)^3 + 3 \)
-
find \\(\\int(6x^4 + 3x^7)dx\\) \\(\\square\\) + c
$\frac{6}{5}x^5 + \frac{3}{8}x^8$
-
solve this system of equations by graphing. first graph the equations, …
The solution is $(2, 4)$
-
subtract: 9 - -5 =
14
-
subtract: 8 - 6 = submit
2
-
graph the following function on the axes provided. $f(x) = \\begin{case…
# Explanation: ## Step1: Graph \( y = -x + 1 \) for \( x \leq -3 \) First, find the endpoint at \( x = -3 \). Substitute \( x = -3 \) into \( y = -x + 1 \): \( y = -(-3) + 1 = 3 +…
-
graph the following function on the axes provided. $f(x) = \\begin{case…
The graph consists of: - A line segment from \((1, -3)\) (closed circle) to \((5, 5)\) (open circle) for \(1 \leq x < 5\). - A closed circle at \((5, -6)\) for \(x = 5\). - A hori…
-
the velocity of an object moving in a straight line, in meters per minu…
$7$
-
question graph the following function on the axes provided. \\( f(x) = …
To graph the piecewise function: 1. For \( -6\leq x<-2 \): Plot a closed circle at \((-6, 7)\), an open circle at \((-2, 3)\), and draw a line connecting them (using \( y=-x + 1 \…
-
the function ( f ) is shown below. what is the value of ( int_{-2}^{5} …
8
-
2.1 change in arithmetic and geometric sequences ap precalculus name: f…
The \(65^{\text{th}}\) term of the sequence \(\{107, 97, 87, 77, \dots\}\) is \(\boxed{-533}\).
-
express the function graphed on the axes below as a piecewise function.…
\(f(x)=\begin{cases}-\frac{3}{2}x - 6& \text{for }x\leq - 4\\-\frac{3}{2}x+\frac{7}{2}& \text{for }x>5\end{cases}\)
-
express the function graphed on the axes below as a piecewise function.…
\[ f(x)=\begin{cases} -\dfrac{1}{2}x + 5, & x\leq - 2\\ 6, & - 2\lt x\leq3 \end{cases} \]
-
graph the system below and write its solution. \\begin{cases} y = \\fra…
No solution
-
find $f^{-1}(-8)$.\ \ | $x$ | $f(x)$ |\ | --- | --- |\ | $-4$ | $6$ |\ …
15
-
question find $f^{-1}(g(13))$. \\begin{tabular}{|c|c|c|} \\hline $x$ & …
16
-
find $f(f^{-1}(1))$. | $x$ | $f(x)$ | | --- | --- | | $1$ | $8$ | | $9$…
\( 1 \)
-
graph the system below and write its solution.\\begin{cases} y = -2x - …
Infinitely many
-
add. -52 + (-39) = -42 + 43 =
$-52 + (-39) = -91$ $-42 + 43 = 1$
-
evaluate the following. -3 × 5 = 32 ÷ (-4) =
$-3 \times 5 = -15$ $32 \div (-4) = -8$
-
solve the following system of equations graphically on the set of axes …
The solution to the system is $(2, 2)$ (the intersection point of the two lines plotted using their intercepts: $y=-x+4$ uses $(0,4)$ and $(4,0)$; $y=\frac{5}{2}x-3$ uses $(0,-3)$…
-
question let f be the function graphed below. if three subintervals of …
Width of each subinterval: $2.5$ (To complete the right Riemann sum rectangles: draw three rectangles over subintervals $[1,3.5]$, $[3.5,6]$, $[6,8.5]$ with heights equal to the f…
-
which of these represents a function with the following properties? - d…
$f(x)=\frac{3x+1}{3x-1}$ --- ### Second Question
-
which of the following is a complex zero of the polynomial function $p(…
$-2 - \sqrt{2} \cdot i$ --- ### Second Question (Average Rate of Change)
-
5) \\( \\int \\frac{1}{\\sqrt{1 - t^2}} dt \\)\ 7) \\( \\int \\frac{x^3…
$\arcsin(t)+C$ (where $C$ is the constant of integration) ### Problem 7:
-
the piecewise-linear function, f, defined on ( 0 leq x leq 8 ) is shown…
$f(g(4))$
-
solve each math problem to learn facts o 1. this years game will take p…
1
-
consider the rational function $r(x)=-\frac{2x}{x + 3}$. which of the f…
$\boldsymbol{\lim_{x\to-\infty} r(x) = -2}$ $\boldsymbol{\lim_{x\to\infty} r(x) = -2}$
-
graph the function ( h(x) = 2x - 5 ).
# Explanation: ## Step1: Identify the function type The function \( h(x) = 2x - 5 \) is a linear function in the form \( y = mx + b \), where \( m = 2 \) (slope) and \( b = -5 \) …
-
11) $7.7 \\times 9.1$ 12) $3.2 \\times 2.1$ 13) $72.5 \\times 9.9$ 14) …
\( 70.07 \) ### 12) \( 3.2 \times 2.1 \)
-
review the details below. during the middle ages, a hosts generosity wh…
Since foreign spices were difficult to obtain, they became a status symbol for affluent European families.
-
modeling with mathematics a person sitting in the top row of the bleach…
\( 1.2 \)
-
graph the following equations equation 1: ( y = x + 2 ) equation 2: ( y…
To graph the equations: - For \(y = x+2\), plot \((0,2)\) and use slope \(1\) to draw the line. - For \(y=-2x - 4\), plot \((0,-4)\) and use slope \(-2\) to draw the line. - For \…
-
Question was provided via image upload.
\((-2, 0)\) ### 2. Intersection of Equation 4 (\(y = -\frac{1}{4}x + 3\)) and Equation 2 (\(y = -2x - 4\))
-
15 graph the given system of linear equations. ( 18x + 3y = -9 ) ( x - …
To graph the system $\begin{cases}18x + 3y=-9\\x - y=-4\end{cases}$, we convert to slope - intercept form: $y=-6x - 3$ (from $18x + 3y=-9$) and $y=x + 4$ (from $x - y=-4$). Plot t…
-
you must submit thorough, handwritten work. you may only use a writing …
The zeroes of \(f(x)\) are \(5\), \(i\sqrt{6}\), and \(-i\sqrt{6}\).
-
find an ordered pair (x, y) that is a solution to the equation. 2x - y …
\((3, 0)\) (Note: There are other possible solutions, for example, if we choose \( x = 4 \), then \( 2\times4 - y = 6 \) gives \( 8 - y = 6 \), so \( y = 2 \), and the ordered pai…
-
12 graph the given system of linear equations. $y = -1$ $y = -\frac{5}{…
To graph \( y=-1 \) (a horizontal line at \( y = - 1 \)) and \( y=-\frac{5}{2}x + 4 \) (a line with \( y \)-intercept \( (0,4) \) and slope \( -\frac{5}{2} \)): - For \( y=-1 \): …
-
write a slope - intercept equation for a line that passes through (-4, …
$y = -3x - 11$
-
solve the following system of equations graphically on the set of axes …
The solution to the system of equations is \( x = 2 \), \( y=-1 \) or the point \( (2,-1) \).
-
solve the system of equations by graphing. \\begin{cases} y = \\dfrac{2…
The solution to the system is \( (3, 5) \)
-
graph the equations ( y = 3x - 12 ) and ( y = 4x + 3 ) using a graphing…
Correct graph: A Solution to the system: A. The solution is $x = -15$, $y = -57$.
-
solve the system of equations graphically. \\(\\begin{cases} y = 3x - 1…
A. <The graph labeled A with two lines intersecting in the lower left region of the viewing window>
-
compare ( f(x) = x + 2 ) shown in the table below and ( g(x) = 2^x ) sh…
- The y-intercept of $f(x)$ is **greater than** the intercept of $g(x)$. - $g(x)$ is greater than $f(x)$ when $x$ is **greater than 2**
-
graph the rational function. give the domain and range, and discuss sym…
s: - Vertical Asymptotes: C. There are no vertical asymptotes. - Horizontal Asymptote: A. The function has a horizontal asymptote whose equation is \(y = 0\) - Symmetry: B. It is …
-
graph the rational function. give the domain and range, and discuss sym…
\( (-\infty, \infty) \) ### Vertical Asymptotes
-
graph the function below to find the y-intercept and state the domain, …
A) The y-intercept is 3. C) Domain: all real numbers; Range: $y > 0$ F) The asymptote is $y = 0$
-
graph the function below to find the y-intercept and state the domain, …
A) The y-intercept is -4. D) Domain: all real numbers; Range: $y < 0$ F) The asymptote is $y = 0$.
-
graph the rational function. give the domain and range, and discuss sym…
(for domain): \((-\infty, \infty)\)
-
graph the rational function. give the domain and range, and discuss sym…
\((-\infty, \infty)\)
-
find the slope from two points super bowl crack the code directions: fi…
To solve for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\), we use the slope formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let's calculate the slope for each set …
-
use a calculator to find the value of the trigonometric expression. \\c…
7.1853
-
this question has two parts. first, answer part a. then, answer part b.…
A) The y-intercept is 1000. C) The asymptote is y = 0. F) $D = \{x|x \geq 0\}, R = \{y|y \geq 1000\}$
-
use tables and graphs to compare and contrast $f(x) = 2 \\cdot 3^x + 1$…
- For all real numbers in the domain, **both** function(s) is/are increasing. - About the y-axis the functions **are not** symmetric. - As $x$ approaches $-\infty$ the functions h…
-
_______ is when americans had to limit use of key resources like sugar,…
C. Rationing (assuming the options are labeled with C for the green "Rationing" option; if the original option labels are different, adjust the identifier but the text is "Rationi…
-
linear, quadratic, and exponential models #3 observe using graphs and t…
(Part a): Yes, the values of \( 2x^3 + 1 \) remain larger than \( 2^x \) when the table is extended to whole numbers up to ten.
-
selection test (online): teens and technology share a future part a whi…
B. It gives humans almost limitless abilities. ### Part B
-
selection test (online): teens and technology share a future first read…
B. types of math
-
when the celsius temperature is 30°, the corresponding fahrenheit tempe…
\(\frac{9}{5}C + 32\)
-
find the slope and the y-intercept of the graph of the linear equation.…
The slope is $\frac{3}{4}$ The slope-intercept equation is $y=\frac{3}{4}x - 2$
-
0.46 ÷ 0.2 =
2.3
-
suppose that the functions r and s are defined for all real numbers x a…
$(r+s)(x) = 8x + 4$ $(r \cdot s)(x) = 15x^2 + 20x$ $(r-s)(3) = 2$
-
adding and subtracting fractions mini - lesson review the steps for add…
Step 1: Rewrite mixed numbers and whole numbers as improper fractions. Step 2: Find a common denominator. Step 3: Rewrite the fractions as equivalent fractions with the common den…
-
function operations given the function $f(x) = 2x - 4$ and the function…
$10f(3)+g(7)=363$ $g(4)-12f(5)=58$ $f(8)\cdot g(12)=11256$ $\frac{g(2)}{5f(10)}=\frac{3}{5}$
-
15. the graph has points (0, -1), (1, -2), (2, -4) and is a curve on th…
The equation of the function is \( y = -2^x \)
-
use a calculator to find the value of the trigonometric expression.\\ta…
-0.1584
-
9.6 ÷ 0.8 =
12
-
use the graph of the function f given to answer the questions. if there…
The local minimum is \(y=\boxed{-16}\)
-
worksheet: graphing tangent functions directions: graph each tangent fu…
1. **$y=\tan(x)$**: Asymptotes at $x=\frac{\pi}{2}+k\pi$ ($k\in\mathbb{Z}$), period $\pi$, passes through $(0,0)$, increases to $+\infty$ left of $\frac{\pi}{2}$ and $-\infty$ rig…
-
use a calculator to find the value of the trigonometric expression.\\(\…
0.1987
-
a car enthusiast learns that a particular model of car, which costs $34…
\(\$6124.42\)
-
write an equation (a) in slope - intercept form and (b) in standard for…
(a) Slope - intercept form: \(y=\frac{5}{2}x+\frac{13}{2}\) (b) Standard form: \(5x - 2y=-13\)
-
solve the following system of equations graphically on the set of axes …
The solution to the system of equations is the point of intersection of the two lines, which is \( (-2,5) \)
-
find the slope and y-intercept of the given line, and graph it. 3y = -7…
\((0,0)\)
-
solve the system of equations graphed on the coordinate axes below. $y …
The solution to the system is \( x = -6 \), \( y = -4 \) or the ordered pair \( (-6, -4) \)
-
solve the system of equations graphed on the coordinate axes below. $y …
The solution to the system is \( (0, -1) \)
-
find the slope and y-intercept of the line with equation 5x - y = 3. th…
\(5\)
-
4/20 use the given equation to complete the table. ( y = \frac{2}{3}x -…
When \( x = 6 \), \( y = 3 \); when \( x=-3 \), \( y=-3 \); when \( x = 0 \), \( y=-1 \); when \( x = 3 \), \( y = 1 \) If we consider the number labels, and assume the \( x \) va…
-
the piecewise function (problems 5–7) $f(x)=\\begin{cases}3x, & x < 0 \…
\( f(-1) = -3 \) ### Problem 6: Evaluate \( f(3) \)
-
lesson objective students will evaluate piecewise functions by determin…
\( -1 \) ### Problem 2: Evaluate \( f(-2) \)
-
write an equation for the line described. give the answer in standard f…
$9x + y=21$
-
write an equation of the line passing through (-4,7) and having slope -…
$y=-8x - 25$
-
write an equation for the line described. give the answer in slope - in…
$y = 6x+15$
-
the graph of a linear function f is shown to the right. (a) identify th…
The \(x\) - intercept is \((12,0)\)
-
f(x) = \\begin{cases} x^2 - 1, & x < 0 \\\\ 2x, & 0 \\leq x \\leq 4 \\\…
s: 7. \( f(0) = \boldsymbol{0} \) 8. \( f(1) = \boldsymbol{2} \) 9. \( f(4) = \boldsymbol{8} \) 10. \( f(6) = \boldsymbol{9} \)
-
piecewise function (problems 7-10) $f(x)=\\begin{cases}x^2 - 1, & x < 0…
\( f(0)=0 \) ### Problem 8: Evaluate \( f(1) \)
-
the graph of a linear function f is shown a. identify the slope, y-inte…
\( f(x) = -4x + 8 \)
-
the graph of a linear function f is shown a. identify the slope, y-inte…
(0, 8)
-
lesson objective students will evaluate piecewise functions by identify…
\( -3 \) ### Problem 2: Evaluate \( f(0) \)
-
the graph of a linear function f is shown. a. identify the slope, y-int…
\(-4\)
-
1）3.5 ÷ 7 =
0.5
-
29) are these equal? why or why not? \\(\\displaystyle \\sum_{x=1}^{50}…
Yes, they are equal. Because we can use the substitution \( y=x - 20 \) in the second sum, which transforms \( \sum_{x = 21}^{70}\frac{1}{x - 20} \) into \( \sum_{y = 1}^{50}\frac…
-
identify the graph of the following equation. $y = \\frac{1}{3}x + 4$ c…
A. (The graph in option A which has a positive - sloped line crossing the y - axis at \( y = 4 \) and rising from left to right)
-
9. what laws or guidelines exist to protect teen workers, and how do th…
Key laws/guidelines and their hazard-reduction impacts include: 1. U.S. Fair Labor Standards Act (FLSA): Limits work hours, bans teens from high-risk jobs, sets minimum wage, prev…
-
\\int_{0}^{3\\pi/8} \\sin\\left(2x - \\frac{\\pi}{4}\ ight) dx
\(\frac{\sqrt{2}}{4}\)
-
solve the following system of equations graphically on the set of axes …
The solution (intersection point of the two lines) is $(-2, 4)$. To plot the lines: 1. For $y=-x+2$, plot points $(0,2)$ and $(2,0)$, then draw the line through them. 2. For $y=\f…
-
the function below, ( f(x) ), has ( (x - 7) ) and ( (x + 4i) ) as facto…
# Explanation: ## Step1: Analyze given factors We know that if \((x - 7)\) is a factor, then \(x = 7\) is a real zero. For the factor \((x + 4i)\), since complex zeros come in con…
-
solve the following system of equations graphically on the set of axes …
The solution (intersection point) is $(6, 5)$ To plot: 1. For $y=-\frac{1}{2}x+8$: mark $(0,8)$ and $(2,7)$, draw the line through them. 2. For $y=2x-7$: mark $(0,-7)$ and $(4,1)$…
-
two functions are shown below.\\( f(x) = 2x^2 + 2x - 3 \\)\\( g(x) = -0…
D. \(3x(4x - 9y)(4x + 9y)\) Now, let's solve the problem about the function \(H(x) = 4x^3 - 5x^2 - 23x + 6\) (question 9) to find the distance between the two closest real zeros.