微積分
極限、導関数、最適化、関数挙動。
-
11. $12 + 5 \\div 8 + 24 \\div 8 + 4^2 \\div 8$ 12. $3(4.5 + 7.2) - 5 \…
11. $17.625$ (or $\frac{141}{8}$) 12. $15.1$
-
for each part, determine if y is a function of x. (a) a scientist is ru…
\( y \) is a function of \( x \). ### Part (b)
-
u may draw an area model to help you. 8. $504\\div6 = (\\underline{quad…
\(504\div6=(480 + 24)\div6=(480\div6)+(24\div6)=80 + 4 = 84\) So the blanks are filled as follows: \(480\), \(480\), \(6\), \(80\), \(4\), \(84\) (in order of the blanks in the pr…
-
f(x) = sin(x² + 1)
\( f'(x) = 2x\cos(x^{2}+1) \)
-
name date evaluate. a. $2(50 - 4 \\cdot 3^2)$ b. $\\frac{5}{2^3 + 1} + …
a. $28$ b. $\frac{5}{9}$
-
for problems 8–10, evaluate. 8. $312 - (4 + 1)$ 9. $4 cdot |9 - 5| + 6$…
8. $21$ 9. $22$ 10. $3$
-
trish is solving for the zeros of the quadratic function $f(x) = 2x^2 -…
No, the function has no real number zeros.
-
this table of values represents a linear function. x | y 2 | -1 4 | -5 …
\( y=-2x + 3 \)
-
what is the slope of this line? (1, 3) (5, 3)
The slope of the line is \( 0 \).
-
find the slope of the line that passes through (9, 10) and (2, 1). simp…
\( \frac{9}{7} \)
-
5 type the correct answer in the box. use numerals instead of words. if…
1
-
solve the system of equations graphed on the coordinate axes below. $y …
The solution to the system is \( (0, 2) \)
-
solve the system of equations graphed on the coordinate axes below. $y …
The solution to the system is \( (0, 2) \)
-
what is the slope of this line? simplify your answer and write it as a …
\(\frac{1}{2}\)
-
what is the slope of this line? simplify your answer and write it as a …
\(\frac{1}{2}\)
-
do these problems in your head. use paper only for the problems that yo…
1. $102$ 2. $460$ 3. $171$ 4. $35000$ 5. $144000$ 6. $6.1$ 7. $10.6$ 8. $0.98$ 9. $1.67$
-
find the quotient. \\(4\\enclose{longdiv}{231.2}\\)
57.8
-
graph the line with the equation $y = -x + 6$.
# Explanation: ## Step1: Identify the slope and y-intercept The equation \( y = -x + 6 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is th…
-
graph the line with the equation $y = -x + 6$.
# Explanation: ## Step1: Identify the slope and y-intercept The equation \( y = -x + 6 \) is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is th…
-
given the function below, fill in the table of values, use the table of…
# Explanation: ## Step1: Calculate $\sqrt[3]{x}$ for $x=-8$ $\sqrt[3]{-8} = -2$ ## Step2: Calculate $y$ for $x=-8$ $y = -2 - 4 = -6$ ## Step3: Calculate $\sqrt[3]{x}$ for $x=-1$ $…
-
use technology to find points and then graph the function $y = \\sqrt{x…
Four points to plot: $(-1, 0)$, $(0, 1)$, $(3, 2)$, $(8, 3)$ (The graph is a right-opening square root curve starting at $(-1, 0)$ and increasing slowly as $x$ increases.)
-
sketch the graph of the quadratic function $f(x) = x^2 - 4x + 3$, label…
- Vertex: $(2, -1)$ - x-intercepts: $(1, 0)$ and $(3, 0)$ - y-intercept: $(0, 3)$ - Axis of symmetry: $x=2$ *(To sketch the graph: Plot the intercepts and vertex, draw a upward-op…
-
sketch the graph of the quadratic function $f(x) = x^2 - 4x + 3$, label…
- Vertex: $(2, -1)$ - x-intercepts: $(1, 0)$ and $(3, 0)$ - y-intercept: $(0, 3)$ - Axis of symmetry: $x=2$ *(To sketch the graph: Plot the intercepts and vertex, draw a upward-op…
-
given the function below, fill in the table of values, use the table of…
# Explanation: ## Step1: Calculate $\sqrt[3]{x}$ for $x=-8$ $\sqrt[3]{-8} = -2$ ## Step2: Calculate $y$ for $x=-8$ $y = -2 - 4 = -6$ ## Step3: Calculate $\sqrt[3]{x}$ for $x=-1$ $…
-
graph the following function on the axes provided. $f(x) = \\begin{case…
The piecewise function is graphed as: 1. A line segment with an open endpoint at $(-2, 3)$ and a closed endpoint at $(1, 6)$ (for $f(x)=x+5$, $-2<x\leq1$) 2. A line segment with o…
-
identify the equation for the graph. $y - 3 = sqrt3{x}$, $y + 3 = sqrt3…
\( y + 3=\sqrt[3]{x} \)
-
identify the equation for the graph. $y - 3 = sqrt3{x}$, $y + 3 = sqrt3…
\( y + 3=\sqrt[3]{x} \)
-
5 type the correct answer in the box. use numerals instead of words. if…
1
-
find the quotient. \\(4\\enclose{longdiv}{231.2}\\)
57.8
-
graph the following function on the axes provided. $f(x) = \\begin{case…
The piecewise function is graphed as: 1. A line segment with an open endpoint at $(-2, 3)$ and a closed endpoint at $(1, 6)$ (for $f(x)=x+5$, $-2<x\leq1$) 2. A line segment with o…
-
graph $y = \\frac{4}{5}x - 7$.
To graph \(y=\frac{4}{5}x - 7\): 1. Plot the y - intercept \((0,-7)\). 2. Use the slope \(\frac{4}{5}\) (rise = 4, run = 5) to find another point (e.g., from \((0,-7)\), moving up…
-
suppose f(x) > 0 for all x and \\(\\int_{0}^{9} f(x) dx = 18\\). let r …
The correct integral setup (assuming a misprint and rotating around the \(x\) - axis) is \(\pi\int_{0}^{9}(f(x^{2}))^{2}dx\), so the answer is the option with \(\int_{0}^{9}(f(x^{…
-
review the graph of ( f(x) = sqrt3{x} ) and the graph of the transforme…
-2f(x + 4)
-
b) what is one - half of one - half? show your work
$\frac{1}{4}$
-
9. prove each identity. a) \\(dfrac{cos^2 \theta - sin^2 \theta}{cos^2 …
$\frac{\cos^2\theta - \sin^2\theta}{\cos^2\theta + \sin\theta\cos\theta}=1 - \tan\theta$，等式得证。
-
for which x - values is the graph below discontinuous? options: {…-3, -…
$\{\dots -3, -1, 1, 3, \dots\}$
-
graph $y = \\dfrac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. From \( (0,-7) \), use the slope \( \frac{4}{5} \) to find another point: move up 4 units and righ…
-
graph $y = \\frac{4}{5}x - 7$.
To graph \(y=\frac{4}{5}x - 7\): 1. Plot the y - intercept \((0,-7)\). 2. Use the slope \(\frac{4}{5}\) (rise = 4, run = 5) to find another point (e.g., from \((0,-7)\), moving up…
-
26 graph the function $f(x) = x^2 + 4x + 3$. state the equation of the …
Axis of symmetry: $x = -2$ Graph key points: Vertex $(-2, -1)$, x-intercepts $(-1, 0)$, $(-3, 0)$, y-intercept $(0, 3)$
-
26 graph the function $f(x) = x^2 + 4x + 3$. state the equation of the …
Axis of symmetry: $x = -2$ Graph key points: Vertex $(-2, -1)$, x-intercepts $(-1, 0)$, $(-3, 0)$, y-intercept $(0, 3)$
-
26 graph the function $f(x) = x^2 + 4x + 3$. state the equation of the …
Axis of symmetry: $x = -2$ Key points for graph: $(-3,0), (-2,-1), (-1,0), (0,3), (-4,3)$
-
graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point: from \( (0,-7) \), move up 4 and right 5 to…
-
graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move 4 up and 5 right…
-
graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept at \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find another point (e.g., from \( (0,-7) \), move up 4 and righ…
-
graph $y = \\frac{4}{5}x - 7$.
要绘制\(y = \frac{4}{5}x - 7\)的图像： 1. 标记\(y\)轴截距点\((0, -7)\)（因为当\(x = 0\)时，\(y = -7\)）。 2. 利用斜率\(\frac{4}{5}\)（上升\(4\)，向右\(5\)），从\((0, -7)\)开始，向右移动\(5\)个单位，向上移动\(4\)个单位，得到点\((5, -3)\…
-
what is \\(\\lim_{h \\to 0} \\frac{8\\left(\\frac{1}{2} + h\ ight)^8 - …
1
-
sketch the graph of $f(x) = x^2 - 4x + 3$.
The graph is an upward-opening parabola with: - Vertex at $(2, -1)$ - x-intercepts at $(1, 0)$ and $(3, 0)$ - y-intercept at $(0, 3)$ (Plot these points and draw a smooth symmetri…
-
1. what does absolute value mean? please make a function table and grap…
1. The absolute value of a number, denoted as $|x|$, is the non-negative value of $x$ without regard to its sign. Mathematically, $|x| = \begin{cases} x & \text{if } x \geq 0 \\ -…
-
identify the graph for the equation. y = 9(3)^x
The third graph (the right - most graph among the three given graphs) is the graph of \( y = 9(3)^x \)
-
find the inverse function. f(x) = 3x - 1 f⁻¹(x) = (x + ?) / ?
The numerator's box should be 1 and the denominator's box should be 3. So \( f^{-1}(x)=\frac{x + \boldsymbol{1}}{\boldsymbol{3}} \)
-
using the following equations, find g(f(x)): f(x) = -x² - 1 g(x) = x + …
The coefficient of \( x^2 \) is \(-1\) and the constant term is \(4\), so \( g(f(x)) = \boxed{-1}x^2 + \boxed{4} \)
-
graph $y = \\frac{4}{5}x - 7$.
To graph \( y=\frac{4}{5}x - 7 \): 1. Plot the y - intercept \( (0,-7) \). 2. Use the slope \( \frac{4}{5} \) to find additional points (e.g., \( (5,-3) \) by moving 5 right and 4…
-
identify the equation for the graph. $y = (x - 1)(x - 3)^2(x - 5)$ $y =…
\(y=(x - 1)(x - 3)^{2}(x - 5)\) (the first option)
-
solve the following system of equations graphically on the set of axes …
The solution to the system of equations is \( x = -6 \), \( y = 1 \) (or the point \( (-6, 1) \)).
-
solve the system of equations graphed on the coordinate axes below. y =…
The solution to the system of equations is \( x = 1 \), \( y = 3 \) or the ordered pair \( (1, 3) \)
-
14. which of the following terms describe the graph shown? select all c…
A. linear D. decreasing E. function
-
answer all questions in this part. each correct answer will receive 2 c…
4 ### Question 2
-
attempt 1: 10 attempts remaining. let ( f(x) = 2x^2 - 2x - 7 ). (a) com…
(a): \( 4x + 2h - 2 \) ### Part (b)
-
attempt 1: 10 attempts remaining. given ( f(x) = e^x - 3 ), use the dif…
\( 1.822 \)
-
attempt 1: 10 attempts remaining. given ( f(x) = -6x^2 + 7x - 3 ), use …
\(-5\)
-
attempt 1: 10 attempts remaining. let ( f(x) = x^2 ). compute the value…
\( 10.04 \)
-
attempt 1: 10 attempts remaining. given ( f(x) = 5x - 7 ), use the diff…
5
-
quiz yourself as you complete multiple - choice questions, theyll becom…
B. a way to quiz yourself
-
attempt 1: 10 attempts remaining. given the function $f(x) = 2 + 5x^2$,…
s: - \( f(a) = \boldsymbol{2 + 5a^2} \) - \( f(a + h) = \boldsymbol{2 + 5a^2 + 10ah + 5h^2} \) - \( \frac{f(a + h) - f(a)}{h} = \boldsymbol{10a + 5h} \) (for \( h eq0 \))
-
attempt 1: 10 attempts remaining. find the difference quotient for the …
\( 1 \)
-
attempt 1: 10 attempts remaining. the function $f(x) = \\frac{x^2 - 8}{…
\( 5 \)
-
what value does $f(x) = \\frac{1}{(x - 7)^2}$ approach as $x \\to 7$? (…
\(\infty\)
-
this is the graph of a linear inequality. write the inequality in slope…
\(y\geq-\frac{1}{2}x - 4\)
-
-\frac{4.99^{2}}{4}+3(4.99)+7 =\\ -\frac{4.999^{2}}{4}+3(4.999)+7 =
s: First expression: $\boldsymbol{15.744975}$ Second expression: $\boldsymbol{15.74949975}$
-
$-\frac{5.061^{2}}{4}+3(5.001)+7=$
\(15.59956975\)
-
$-\frac{5.1^{2}}{4}+3(5.1)+7=$
15.7975
-
-\frac{5.01^{2}}{4}+3(5.01)+7=
\(15.754975\)
-
-\frac{5.01^{2}}{4}+3(5.01)+7=
\(15.754975\)
-
$-\frac{5^{2}}{4}+3(5)+7 =$
\(\frac{63}{4}\) (or \(15.75\))
-
$-\frac{4.9^{2}}{4}+3(4.9)+7=$
\(15.6975\)
-
-\frac{4.9^{2}}{4}+3(4.9)+7; -\frac{4.99^{2}}{4}+3(4.99)+7; -\frac{4.99…
For \(-\frac{5^2}{4}+3(5)+7\), the result is \(15.75\) (or \(\frac{63}{4}\)). For \(-\frac{4.9^2}{4}+3(4.9)+7\), the result is \(15.6975\). For \(-\frac{5.01^2}{4}+3(5.01)+7\), th…
-
this is the graph of a linear inequality. write the inequality in slope…
\(y\geq - x\)
-
this is the graph of a linear inequality. write the inequality in slope…
$y \geq -\frac{3}{2}x + 6$
-
question 10 of 10 according to the tenth amendment, the powers of ____ …
D. the federal government
-
complete the table of values for the functions $f(x) = \\frac{1}{2}|x|$…
(Table Completion): | \( x \) | \( f(x) \) | \( g(x) \) | |---------|------------|------------| | \( -2 \) | \( 1 \) | \( 0.25 \) | | \( -1 \) | \( 0.5 \) | \( 0.5 \) | | \( 0 \) …
-
complete the table of values for the functions $f(x) = \\frac{1}{2}|x|$…
(Table Completion): | \( x \) | \( f(x) \) | \( g(x) \) | |---------|------------|------------| | \( -2 \) | \( 1 \) | \( 0.25 \) | | \( -1 \) | \( 0.5 \) | \( 0.5 \) | | \( 0 \) …
-
complete the table of values for the functions $f(x) = 2|x|$ and $g(x) …
### Part 1: Completing the table of values for \( f(x) = 2|x| \) and \( g(x) = x^2 - 1 \) #### For \( x = -3 \): - **Calculating \( f(-3) \):** The function is \( f(x) = 2|x| \). …
-
f) range 11. a) sketch ( f(x) = sqrt3{x + 1} ) b) domain: range: c) alg…
a) (Sketch: Plot points $(-1,0)$, $(0,1)$, $(-9,-2)$, $(7,2)$ and draw a smooth cube root curve shifted left 1 unit; also draw $y=x$ as a dashed line for reference) b) Domain: $(-…
-
complete the table of values for the functions $f(x) = x^2 - 2$ and $g(…
### Part 1: Complete the table for \( f(x) = x^2 - 2 \) and \( g(x) = |x - 2| \) #### For \( x = 0 \): - \( f(0) = 0^2 - 2 = -2 \) - \( g(0) = |0 - 2| = 2 \) #### For \( x = 1 \):…
-
division introduction part 2 of 2 1 2 trying to earn do these problems …
$95.6 \div 10 = 9.56$ $5566.3 \div 10 = 556.63$ $7.8 \div 10 = 0.78$ $7.9 \div 10 = 0.79$ $98.9 \div 100 = 0.989$ $0.045 \div 10 = 0.0045$ $4 \div 100 = 0.04$ $662 \div 10 = 66.2$…
-
complete the table of values for the functions ( f(x) = |2x| ) and ( g(…
to \( f(x) = g(x) \): between \( x = -2 \) and \( x = -1 \)
-
complete the table of values for the functions $f(x) = |x - 10|$ and $g…
### Part 1: Completing the table for \( f(x) = |x - 10| \) and \( g(x) = \frac{1}{2}(x - 6)^2 \) #### For \( f(x) = |x - 10| \): - **Step 1: When \( x = 5 \)** Substitute \( x = 5…
-
complete the table of values for the functions $f(x) = \\frac{5}{4}x$ a…
### Part 1: Completing the table for \( f(x) = \frac{5}{4}x \) and \( g(x) = \frac{1}{4}x^2 + 1 \) #### For \( f(x) = \frac{5}{4}x \): ## Step 1: When \( x = -2 \) Substitute \( x…
-
complete the table of values for the functions $f(x)=|x + 4|$ and $g(x)…
to \( f(x) = g(x) \) solution: The equation \( f(x) = g(x) \) has a solution **between \( x = -2 \) and \( x = -1 \)**.
-
complete the table of values for the functions $f(x) = 1.5x$ and $g(x) …
s: #### Table Completion: - \( x = -2 \): \( f(x) = \boldsymbol{-3} \), \( g(x) = \boldsymbol{-1} \) - \( x = -1 \): \( f(x) = \boldsymbol{-1.5} \) (or \( -\frac{3}{2} \)), \( g(x…
-
complete the table of values for the functions $f(x) = -3x + 7$ and $g(…
for \( f(x) = g(x) \): between \( x = 1 \) and \( x = 2 \)
-
complete the table of values for the functions $f(x) = 4|x|$ and $g(x) …
### Part 1: Completing the table for \( f(x) = 4|x| \) and \( g(x) = -2(x - 1)^2 + 12 \) #### For \( f(x) = 4|x| \): - **When \( x = -2 \):** \( f(-2) = 4|-2| = 4 \times 2 = 8 \) …
-
complete the table of values for the functions $f(x) = 2x + 7$ and $g(x…
### Part 1: Completing the table for \( f(x) = 2x + 7 \) and \( g(x) = (x + 1)^2 - 3 \) #### For \( x = -3 \): - **Step 1: Calculate \( f(-3) \)** Substitute \( x = -3 \) into \( …
-
complete the table of values for the functions $f(x) = \\frac{1}{4}|x|$…
### Part 1: Completing the table for \( f(x) = \frac{1}{4}|x| \) and \( g(x) = 2^{x - 1} \) #### For \( f(x) = \frac{1}{4}|x| \): - **When \( x = -3 \):** - Step 1: Calculate \( |…
-
look at the table of values for the functions $f(x) = 3x - 2$ and $g(x)…
between \( x = 0 \) and \( x = 1 \)
-
multiplication introduction part 1 of 2 do these problems in your head.…
$7 \times 10 = 70$ $59 \times 10 = 590$ $100 \times 82 = 8200$ $30 \times 3 = 90$ $90 \times 6 = 540$ $40 \times 5 = 200$ $4 \times 700 = 2800$ $70 \times 900 = 63000$ $50 \times …
-
use the calculator below to approximate \\(\\sqrt{134}\\) as a decimal …
11.6
-
multiplication introduction part 1 of 2 1 2 trying to earn: these probl…
10 10 820 30 60 50 7000 9000 2000 *Note: The first digit of the first six problems is cut off; this solution assumes the leading term for each incomplete problem is 10, consistent…
-
use the calculator below to approximate \\(\\sqrt{134}\\) as a decimal …
$11.5$
-
13. identify if each statement in the table below describes a debit, cr…
| STATEMENT | DEBIT | CREDIT | PREPAID DEBIT | |-----------|-------|--------|---------------| | a. May have overdraft fees | X | | | | b. Spending limit is how much is preloaded o…