微积分
极限、导数、最优化与函数性质。
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verify that ( y = sin 2t + 3cos 2t ) is a solution to the initial value…
\( 2\cos 2t - 6\sin 2t \)
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1. **find the relative extrema of $f(x) = x^3 + 3x^2 - 9x + 5$**
Relative maximum at $x=-3$ with value $32$; relative minimum at $x=1$ with value $0$
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function operations for use with exploration 5.5 essential question how…
(to the Essential Question): To sketch the graph of an arithmetic combination (sum, difference, product, or quotient) of two functions \( f(x) \) and \( g(x) \) using their graphs…
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Question was provided via image upload.
When \( x = 0 \), \( y = 0 \); when \( x = 4 \), \( y = 2 \); when \( x = 10 \), \( y = 5 \)
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consider the indefinite integral \\(\\int x^4 \\cdot \\sqrt2{x^5 - 8} \…
$u = x^5 - 8$ $du = 5x^4$ $\int \frac{1}{5}u^{\frac{1}{2}}$
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y = -4x + 13 x | y 1 | 2 | 3 | click to select points on the graph.
For \( x = 1 \), \( y = 9 \); for \( x = 2 \), \( y = 5 \); for \( x = 3 \), \( y = 1 \)
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4 sketch the graph of each line: $y = -\frac{3}{2}x - 1$
The graph of the line \(y =-\frac{3}{2}x - 1\) is drawn by first plotting the y - intercept \((0,-1)\) and then using the slope \(-\frac{3}{2}\) to find additional points (such as…
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complete the table and then graph the function. $y = 2x$ | x | y | |---…
The completed table has points \((0,0)\), \((2,4)\), \((5,10)\). To graph the function, plot these points and draw a line through them.
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1.1: order of operations score: 5/14 answered: 5/14 question 6 evaluate…
47
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1.1: order of operations score: 4/14 answered: 4/14 question 5 use the …
$(2+3)^2 = 25$ $2^2+3^2 = 13$
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1.1: order of operations score: 3/14 answered: 3/14 question 4 use the …
270
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exercises 1.5 substitution score: 50/170 answered: 5/17 question 6 eval…
$\frac{4}{7}\sin^7(x)$
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question 5 evaluate the integral by making the given substitution. \\(\…
$\frac{1}{4}\sec(4x)$
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exercises 1.5 substitution score: 30/170 answered: 3/17 question 4 eval…
$\frac{(x^6 - 1)^{14}}{84}$
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exercises 1.5 substitution score: 20/170 answered: 2/17 question 3 eval…
$\frac{(x^2+4x+9)^6}{6} + C$
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exercises 1.5 substitution score: 0/170 answered: 0/17 question 1 textb…
True
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20 graph the equation: $y = 2x + 3$
The graph of \( y = 2x + 3 \) is a straight line with a y - intercept at \( (0,3) \) and a slope of 2, passing through points like \( (1,5) \) and \( (-1,1) \) (and others found u…
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fill in the missing number. \\(\frac{4}{5} \times \frac{1}{2} = \frac{2…
5
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a. the free enterprise system is the best economic system because it al…
Producers can decide to make new or better products to attract consumers in the free enterprise system.
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17 graph the equation: $y = -\frac{1}{3}x - 4$
To graph \(y =-\frac{1}{3}x-4\): 1. Plot the y - intercept \((0, - 4)\). 2. Use the slope \(-\frac{1}{3}\) to find another point (e.g., from \((0,-4)\), move down 1 and right 3 to…
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fill in the missing number. \\(\\frac{1}{2} \\times \\frac{4}{5} = \\fr…
5
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match each equation with the sketch of its graph.
To solve this, we analyze each graph's key features (domain, range, starting point, direction) and match with the equation's properties. However, since the equations aren't provid…
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write the slope intercept form of the equation of the line. equation: $…
\(y =-\frac{1}{2}x-1\)
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use technology to find points and then graph the function $y = 2^x - 7$…
Five points with integer coordinates for \( y = 2^x - 7 \) are (0, -6), (1, -5), (2, -3), (3, 1), (4, 9). Plot these points and draw the exponential curve.
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use technology to find points and then graph the function ( y = 2^x - 7…
The graph is drawn by plotting the points \((-3,-6.875)\), \((-2,-6.75)\), \((-1,-6.5)\), \((0, - 6)\), \((1,-5)\), \((2,-3)\), \((3,1)\) and connecting them with a smooth curve, …
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find an explicit formula, f(n), for the following geometric sequence: 2…
$f(n) = 2 \cdot (-3)^{n-1}$
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multiply. 0.07 × 8
0.56
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evaluate the following. (a) $|-7 + 6| = \\square$ (b) $|-7| + 6 = \\squ…
(a) $1$ (b) $13$
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find the inverse of the function: $f(x) = 3x^2 + 8$
The inverse of the function \( f(x) = 3x^2+8 \) is \( f^{-1}(x)=\pm\sqrt{\frac{x - 8}{3}} \) (or equivalent forms like \( f^{-1}(x)=\pm\frac{\sqrt{3x - 24}}{3} \)). If we consider…
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use technology to find points and then graph the function $y = 2sqrt3{x…
Points to plot: (4, -2), (5, 0), (6, 2), (13, 4) (and graph the cube - root function transformed by vertical stretch and horizontal shift)
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peyton steers a remote - control car. the equation $y = 3x + 4$ can be …
Plot the point at the coordinates $(0, 4)$ (on the vertical axis, 4 units above the origin).
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graph the inverse of the provided graph on the accompanying set of axes…
To graph the inverse, follow these steps: 1. **Identify 5 points** on the original linear graph (e.g., estimate coordinates like \((x_1, y_1), (x_2, y_2), \dots\) from the graph).…
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graph the following function on the axes provided. $f(x)=\\begin{cases}…
To graph the piecewise function: 1. For \( -1 < x < 2 \), draw a line segment (using the "Line" tool) with open circles at \( (-1, -8) \) and \( (2, -5) \). 2. For \( 2 < x \leq 5…
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(int_{0}^{8}\frac{dx}{sqrt{1 + x}})
$4\sqrt{2}$
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multiply: $5 \\times \\frac{1}{3}$ provide an answer as a simplified fr…
\(\frac{5}{3}\) (or \(1\frac{2}{3}\))
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express the function graphed on the axes below as a piecewise function.…
\(f(x)=\begin{cases}6x, & x\leq1\\x + 4, & x>4\end{cases}\)
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part of a linear function c is shown below which inequality represents …
C. \( -3 \leq x < 1 \)
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1. estimate the logarithmic $\\log_{3} 220$ to the nearest tenth. type …
1. $4.9$ 2. $2.7$
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which of the following have integer answers when simplified? select all…
## First Question (Select all that apply): - $\sqrt[3]{125}$ - $\sqrt{100}$ - $\sqrt[3]{-8}$ ## Second Question (Simplify $\sqrt[3]{729}$): 9
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in 2023, major league baseball (mlb) introduced several new rules that …
These limitations appeal to spectators because they generate more continuous action and often reduce game times by about thirty minutes.
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write the equation of the line in fully simplified slope - intercept fo…
$y = 2x-2$
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12 - \\frac{4}{5}(5) =
8
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compute. $-2.34 + (-6.52) = $ $-5.6 + 27.4 = $
$-8.86$ $21.8$
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what is the product of (5 - 2i)(3 + i)? the product is.
$17 - i$
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multiply. $-\frac{2}{5}left(-\frac{1}{6} ight)$ write your answer in si…
$\frac{1}{15}$
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compute. -2.34 + (-6.52) = -5.6 + 27.4 =
$-8.86$ $21.8$
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evaluate the following. 43.9 + 1.2² × 0.9
45.196
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a 15-foot ladder is leaning against a wall. if the ladder makes a 78° a…
Approximately 3.12 feet (or exactly $15\cos(78^\circ)$ feet)
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finding slope using rise over run name: date: to find the slope, divide…
For problem (1): Rise ($\Delta y$) = 3 Run ($\Delta x$) = 4 Slope = $\frac{3}{4}$ We can follow a similar process for the other problems: ### Problem (2) ## Step1: Determine Δy Th…
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let $z = 3(cos(15^{circ}) + i sin(15^{circ}))$ and $w = 5(cos(90^{circ}…
z is scaled by a factor of $\frac{1}{5}$ and rotated 90 degrees clockwise.
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why might an author choose an omniscient point of view? a. to create co…
C. To reveal multiple characters' inner thoughts
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what is the equation of the line that passes through the point (3, -8) …
The equation of the line in slope - intercept form is \(y =-\frac{4}{3}x-4\), in point - slope form is \(y + 8=-\frac{4}{3}(x - 3)\) and in standard form is \(4x+3y=-12\) (the mos…
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which of the following functions has the values of ( y ) decreasing as …
A. \( h(x) = 0.3^x \)
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which of the following policies is an example of a present-day debate a…
A. Congress passing the Every Student Succeeds (ESSA) Act that decreased the number of standardized tests
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true or false: $8 + 9 > 17$ true false
False (la opción es la que tiene "False" escrito, es decir, la segunda opción: $\bigcirc$ False)
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why have there been relatively few constitutional amendments? choose 1 …
C. A Constitution Amendment Bill requires more than a simple majority to be ratified
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step 4: draw the line! connect the two points. if i look at the equatio…
1. My line pass through the cross (pass through) the y-axis on $\boldsymbol{3}$. 2. And it has a slope of -4, that means it goes $\boldsymbol{down}$ (rise) 4 times and 1 to the $\…
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solve. 12.25 ÷ 2.5 = □ 4.5 6.5 4.9 0.49
4.9 (the option corresponding to 4.9)
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what is the product of 5.61 and 0.15? 0.8415 0.1625 0.9725 0.2214
0.8415
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how do metaphors and extended metaphors differ? while a metaphor is lim…
A. While a metaphor is limited in length, an extended metaphor is developed over the course of a poem.
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the value of the expression? \\(\frac{1}{2} div 6\\)
\(\frac{1}{12}\)
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4. use the graph to answer each question. a. between which two consecut…
Between points \(D\) and \(E\) the average rate of change is the greatest. ### Part b
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multiple choice: select the choice that completes the statement or answ…
d. The Soviet Union was engaged in an offensive on the Eastern Front. ### Question 2
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3. give a geometrical interpretation of lim (text partially obscured) 4…
Speed is a scalar (magnitude only), but "north" is a direction. The statement incorrectly attributes direction to speed; it should use "velocity" (a vector with magnitude and dire…
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7. use technology to evaluate the logarithm. round your answer to three…
-2.079
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graph the following features: - y-intercept = 2 - slope = $-\frac{6}{5}$
1. Plot the point \((0,2)\) (the y - intercept). 2. From \((0,2)\), move down 6 units and right 5 units to plot \((5,-4)\) (or move up 6 units and left 5 units to plot \((-5,8)\))…
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5. evaluate the logarithm. \\(\\log_{10} 0.001 = \\square\\)
\(-3\)
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when a polynomial has three terms, it is called a ______. the ______ of…
1. trinomial 2. degree 3. addition and subtraction (or simplification)
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micah richard advanced math homework 5 1. \\(\\sqrt{-121}\\) \\(\\sqrt{…
1. $11i$ 3. $\frac{9}{2}i$ 5. $-i$ 7. $-27$ 9. $-384i$ 11. $2+i$ 13. $-19-11i$ 15. $-10-48i$
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18. add: $20\\angle70^{\\circ} + 10\\angle40^{\\circ}$ 19. write $4r - …
$x = 16$, $y = 8$
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use the drawing tools to form the correct answers on the graph. plot th…
Plot the points $(1, 0)$ and $(7, 0)$ on the coordinate graph.
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select the correct answer. if the factors of quadratic function g are (…
A. -3 and 7
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exponential functions - basic question a new car is purchased for 15300…
\(6072.57\)
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use the drawing tool(s) to form the correct answer on the provided grap…
- Vertex: $(1, -9)$ - Axis of symmetry: $x=1$ - Y-intercept: $(0, -8)$ - X-intercepts: $(-2, 0)$ and $(4, 0)$ To plot: 1. Mark the vertex $(1, -9)$ 2. Draw the vertical line $x=1$…
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the functions f and g are defined as follows.\\(f(x) = -5x + 2\\) \\(g(…
\( f(3) = -13 \) \( g(-4) = 60 \)
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2 g(x)=3x² - 3x
Since the problem statement for the function \( g(x) = 3x^2 - 3x \) is incomplete (e.g., we don't know what is being asked about this function, like finding the vertex, roots, der…
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use long division to show that the fraction and decimal in the pair are…
Using long division, we divide 3 by 50. We add two decimal places to 3 (making it 3.00) and divide by 50. 50 goes into 300 (after accounting for the decimal) 6 times, resulting in…
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problem 2 here is a partially fill in the missing d calculations. \\\\b…
The completed division is: $ equire{enclose} \begin{array}{r} 8\ 9 \\ 6 \enclose{longdiv}{5\ 3\ 4} \\ \underline{4\ 8\ \ \ } \\ \ 5\ 4 \\ \ \underline{5\ 4} \\ \ \ 0 \\ \end{array…
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graph $y = 3sqrt3{(x + 1)^2}$ and $y = 20$ to check the solutions of $x…
Neither $x=7$ nor $x=-9$ are solutions to $5\sqrt{(x+1)^2}=20$. The actual solutions (where the graphs intersect) are $x=3$ and $x=-5$.
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the volume of the prism is modeled by function v v(x) = x³ - 12x² + 35x…
$v(x)=x(x-5)(x-7)$
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type the correct answer in the box. find the equation of the line perpe…
\( 2x + 3 \)
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what are the zeros of the graphed function? a. 0 and 4 b. -4, -2, and 0…
C. 0, 2, and 4
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r(x) = 0.05(x² + 1)(x - 6) consider the graph of function r. use the gr…
Function $r$ has two complex zeros and one real zero. Based on the graph, the population decreased between 0 and 6 days and the population increased after 6 days.
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r(x) = 0.05(x² + 1)(x - 6) consider the graph of function r use the gra…
Function $r$ has **two complex zeros** and **one real zero**. Based on the instantaneous growth rate, the population decreased **before 6** days and the population increased **aft…
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r(x) = 0.05(x² + 1)(x - 6) consider the graph of function r. use the gr…
Function $r$ has **one local maximum** and **one local minimum**. Based on the instantaneous growth rate, the population decreased **6** days and the population increased **all da…
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r(x) = 0.05(x^2 + 1)(x - 6) consider the graph of function r. use the g…
Function $r$ has $\boldsymbol{\text{local maximum}}$ and $\boldsymbol{\text{local minimum}}$. Based on the instantaneous growth rate, the population decreased $\boldsymbol{\text{f…
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drag the tiles to the correct boxes. not all tiles will be used. which …
$y = x^4 - 5x^2 + 4$
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what is the inverse of the function $f(x)=2x - 10$? $h(x)=\frac{1}{2}x …
$h(x) = \frac{1}{2}x + 5$
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svlc algebra 1a - essentials (15997) evaluating functions which stateme…
$f(2) = g(-2)$
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farmer jones, and his wife, dr. jones, decide to build a fence in their…
$\frac{44\sqrt{11}}{9}$
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which statement is true regarding the graphed functions? $f(-2) = g(-2)…
$f(0) = g(0)$
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if $f(x) = 6x - 4$, what is $f(x)$ when $x = 8$? 2 16 52 44
44
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what is the inverse of the function $f(x) = \\frac{1}{9}x + 2$? $h(x) =…
$h(x) = 9x - 18$
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what is the inverse of the function $f(x)=2x + 1$? options: $h(x)=\frac…
B. $h(x) = \frac{1}{2}x - \frac{1}{2}$
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evaluate the indefinite integral.\\(int 4e^{4x}sin(e^{4x}) dx\\)\\(\\bo…
$-\cos(e^{4x})$
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evaluate the indefinite integral.\\(\\int x^4 \\sqrt{14 + x^5} dx\\)\\(…
$\frac{2}{15}(14 + x^5)^{\frac{3}{2}}$
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evaluate the indefinite integral.\\(\\int \\frac{7}{(t + 9)^2} dt\\)\\(…
$-\frac{7}{t+9}$
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evaluate the indefinite integral. \\(\\int 2\\sin^3(x)\\cos(x)dx = \\sq…
$\frac{1}{2}\sin^4(x)$
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evaluate the integral \\(\\int x^3 (x^4 - 9)^6 dx\\) by making the subs…
$\frac{(x^4 - 9)^7}{28}$
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find \\(\\int (x + 3)(x - 4) dx\\) \\(\\boxed{}\\) + c
$\frac{x^3}{3} - \frac{x^2}{2} - 12x$