Calculus
Limits, derivatives, optimization, and behavior of functions.
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consider the following polynomial. $s(x) = 4x^2(x + 5)(x - 8)$ step 2 o…
For \(s(x) ightarrow\) \(\boldsymbol{\infty}\) as \(x ightarrow-\infty\) For \(s(x) ightarrow\) \(\boldsymbol{\infty}\) as \(x ightarrow\infty\)
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70. \\(3x^3 - x^2 + x - 2\\) divided by \\(3x^2 + x + 1\\) 72. \\(-3x^4…
The quotient is \(-3x^3 - 3x^2 - 3x - 5\) and the remainder is \(-6\), or \(\frac{-3x^4 - 2x - 1}{x - 1}=-3x^3 - 3x^2 - 3x - 5-\frac{6}{x - 1}\)
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question 19 find \\( \\frac{d}{dx} \\left x^3 \\sin x \ ight \\). \\( \…
\(3x^{2}\sin x + x^{3}\cos x\) (the third option: \(3x^{2}\sin x + x^{3}\cos x\))
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consider the following polynomial inequality. $x^{2}(x + 6)(x - 8) > 0$…
\((-\infty,-6)\cup(8,\infty)\)
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use the elementary properties of logarithms to solve the following equa…
$x = 4$
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the president appoints a new supreme court justice, but the senate refu…
B. It highlights how the Senate can limit the president’s power in appointing officials
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question 16 find \\(\\dfrac{dy}{dx}\\) for \\(y = \\sec x\\). \\(\\circ…
\( \boldsymbol{\frac{dy}{dx}=\sec x\tan x} \) (the last option: \( \frac{dy}{dx}=\sec x\tan x \))
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write the equation of the line in fully simplified slope - intercept fo…
\(y=-x - 1\)
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to take a chance again on real love and gratification from a romantic p…
a) react angrily to being praised
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add. -81.4 + (-12)
$-93.4$
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read the excerpt from the article \gun debate? what gun debate?\ after …
The correct option is: Illustrates how an opposing argument—that reasonable gun restrictions will "send us down a slippery slope to the abolition of all guns in America"—is illogi…
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1. divide 126 ÷ 7 = 18 (long division work shown) 2. fred (partially vi…
$\frac{7}{9} = 0.\overline{7}$ (or approximately $0.78$ if rounding to two decimal places)
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axis of revolution: $x$-axis, $v = \\int_{a}^{b} \\pi \\left( f(x)^2 - …
A. $4x^3 - 15x^2 - 35$
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determine where f is discontinuous. f(x) = \\begin{cases} \\sqrt{-x} & …
O 0 and 7
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problem 8 add. -9.2 + 4.4
-4.8
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find the indicated sum. \\(\\sum_{i = 1}^{6} 4i\\) \\(\\sum_{i = 1}^{6}…
84
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according to the article \how to solve social problems\ this was not a …
D. All are strategies for solving social problems
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let f be a continuous and differentiable function. use this table of va…
8 (corresponding to the option "8")
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read the statement a proposed amendment gives the executive branch the …
B. It would remove separation of powers and give more power to one branch
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this question is designed to be answered without a calculator. let f(x)…
\( -12x^2 \) (corresponding to the option: \( -12x^2 \))
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question 12 evaluate the limit: \\(\\lim\\limits_{c\\to -\\infty} \\fra…
A. \( \frac{3}{7} \)
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this question is designed to be answered without a calculator. if $f(x)…
20
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test prep 7. which expression has a value of 7? a ( 4 + 0.5 \times 8 - …
C. \( 4 + 0.5 \times (8 - 2) \)
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use the given interactions to edit the selected curve.
The equation of the transformed logarithmic curve is \( y=\log_{5}(x)+8 \)
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this question is designed to be answered without a calculator. a partic…
\(-40\space cm/sec^2\) (corresponding to the option: \(-40\space cm/sec^2\))
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test prep 7. which expression has a value of 7? a 4 + 0.5 × 8 − 2 b (4 …
C. \(4 + 0.5 \times (8 - 2)\) ### Question 8
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this question is designed to be answered without a calculator. if $y = …
\(-24\)
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classify whether each example grants or limits the power of the governm…
Grants power: - the division of responsibilities between state and national governments - the authority to raise money for national programs Limits power: - the protection of indi…
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2. (15 points) find the absolute extrema of $f(t) = t\\sqrt{4 - t^2}$ o…
Absolute minimum: \( -\sqrt{3} \) (at \( t = - 1 \)); Absolute maximum: \( 2 \) (at \( t=\sqrt{2} \))
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question 11 evaluate the limit: \\(\\lim_{x\\to 2^+} \\frac{x + 7}{(x -…
\( \infty \) (corresponding to the option with \( \infty \))
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write the equation of this line in slope-intercept form. write your ans…
\( y = -\frac{1}{3}x + 10 \)
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write the first four terms of the sequence $a_n = 2(n + 1)!$ $a_1 = \\s…
The first four terms are \(4\), \(12\), \(48\), \(240\) (with \(a_1 = 4\))
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below are two inequalities and the graphs of their lines without the sh…
A. (2, 0) (assuming this is one of the options; if options differ, adjust accordingly)
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question 10 evaluate the limit: \\(\\lim\\limits_{x\\to 5} \\dfrac{x - …
\( \frac{2}{3} \) (the option with \( 2/3 \))
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write the equation of this line in slope-intercept form. write your ans…
\( y = x + 1 \)
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eghosa starts at -250 feet and climbs up to an elevation of 50 feet. ho…
300
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drag the labels to the correct locations on the image. not all labels w…
\( -\infty < y < \infty \) (with the labels \( -\infty \), \( y \), \( \infty \) placed in the respective boxes: first box \( -\infty \), middle box \( y \), third box \( \infty \…
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question 9 4 pts the integral ( v = pi int_{0}^{pi} left( sqrt{sin x} i…
The integral describes the volume of the solid obtained by rotating the region between \(0 \leq x \leq \pi\) and \(0 \leq y \leq \sqrt{\sin x}\) about the \(x\)-axis. (The option …
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select the correct answer. the graph of the rational function f is show…
A
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if f(x) = 4x⁴ + 3x - 4, then what is the remainder when f(x) is divided…
The remainder is \( 329 \).
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evaluate the indefinite integral: $int cos^{5} x sin x , dx$. $-\frac{1…
\( -\frac{1}{6}\cos^6 x + C \) (the last option: \( -\frac{1}{6}\cos^6 x + C \))
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if $f(x) = x^3 + 12x^2 + 23x - 36$ and $f(-4) = 0$, then find all of th…
The zeros of \( f(x) \) are \( x = -9 \), \( x = -4 \), and \( x = 1 \).
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write the equation of this line in slope-intercept form. write your ans…
$y=-x - 3$
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4. which corner point on this graph will result in the maximum value of…
\(\boldsymbol{(14, -4)}\) (which is the second option, so B. \((14, -4)\))
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the graph of a quadratic function with vertex (1, 0) is shown in the fi…
(a) domain: All reals (or \( -\infty < x < \infty \)) (b) range: \( y\leq0 \)
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write a cosine function that has an amplitude of 3, a midline of y = 4 …
\( f(x) = 3\cos(3\pi x) + 4 \)
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the graph of a quadratic function with vertex (3, 2) is shown in the fi…
(A) range: \( y\geq2 \) (B) domain: All real numbers (or \( (-\infty, \infty) \) or \( x\in\mathbb{R} \))
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(6) use your dictionary to find out what each of the following was: (a)…
The Monroe Doctrine (1823) was a U.S. foreign policy declaring the Americas off - limits to new European colonization and that Europe should not interfere in the Americas’ affairs…
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write the equation of this line in slope-intercept form. write your ans…
\( y=\frac{1}{3}x - 6 \)
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read the excerpt from \mother tongue.\ i’ve heard other terms used, \li…
B. Tan expresses an opinion to support the idea that people who speak nonstandard forms of English are unfairly judged in negative ways.
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let a and b be real numbers where a ≠ b ≠ 0. which of the following fun…
\(f(x)=(x - a)^{2}(x - b)^{4}\)
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read the excerpt from \mother tongue.\ those tests were constructed aro…
C. Tan gives an example of her experience with achievement tests to support the idea that they are not always accurate measures of language ability.
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which point of view does the narrator use in the passage? youre in the …
second person
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1) which point of view does the narrator use in the passage? 1) \let me…
third person omniscient
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which statement describes the graph of f(x) = 4x⁷ + 40x⁶ + 100x⁵? ○ the…
The graph crosses the x - axis at \( x = 0 \) and touches the x - axis at \( x=-5 \) (the third option: The graph crosses the x - axis at \( x = 0 \) and touches the x - axis at \…
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which point of view does the narrator use in the passage? \the sea is s…
first person
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read the excerpt from \mother tongue.\ those tests were constructed aro…
C. Tan believes that achievement tests give inadequate measurements of language ability.
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problem 2: part a create a graph that shows a non - proportional linear…
To create the graph: 1. Use the equation of a non - proportional linear relationship \(y=\frac{1}{4}x + b\) where \(b eq0\) (e.g., \(y=\frac{1}{4}x + 1\)). 2. Plot the \(y\) - in…
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which point of view does the narrator use in the passage? ford stared a…
third person limited
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read the excerpt from \mother tongue.\ and sure enough, the following w…
A. Nonstandard forms of English can be as effective as the standard form of English.
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review 3 winter term name_____________________ per_____ write an equati…
\( y - 2 = 4(x - 1) \) (or \( y+2 = 4x \) is also correct, but \( y - 2=4(x - 1) \) is more in line with using the point \( (1,2) \))
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ex #1: h(x) = (9x^5 + 4)(7x - 5) =
$63x^6 - 45x^5 + 28x - 20$
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radius the radius r in inches of a sphere can be approximated by $r = \…
21
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the graph of a function is shown on the coordinate plane below. identif…
\(2\)
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subtract. ex. \\(\\frac{3}{4} - \\frac{1}{8} = \\frac{6}{8} - \\frac{1}…
(1) \(\frac{3}{4}-\frac{5}{8}=\frac{\boldsymbol{6}}{8}-\frac{5}{8}=\boldsymbol{\frac{1}{8}}\) (2) \(\frac{3}{4}-\frac{3}{8}=\boldsymbol{\frac{3}{8}}\) (3) \(\frac{1}{4}-\frac{1}{8…
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use transformations to graph the following function. determine the doma…
- Transformation: A. The graph of \( y = 6^{x} \) should be shifted vertically up by 4 units. - Domain: \( (-\infty,\infty) \) - Range: \( (4,\infty) \) (corrected from the origin…
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classify each legislation and court case statement to the correct colum…
### Expanded Rights: - Americans with Disabilities Act (1990) – Established protections to prevent unfair treatment in public spaces, employment, and services - 24th Amendment (19…
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use transformations to graph the following function. determine the doma…
A. The graph of \( y = 6^{x} \) should be shifted vertically up by 4 units. \((4,\infty)\)
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subtract. (1) (\frac{4}{5} - \frac{1}{5} =) (2) (1\frac{3}{5} - \frac{2…
(1) \(\frac{3}{5}\) (2) \(1\frac{1}{5}\) (3) \(2\frac{2}{5}\) (4) \(1\) (5) \(\frac{5}{9}\) (6) \(2\frac{3}{7}\) (7) \(1\frac{3}{8}\) (8) \(2\)
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use transformations to graph the following function. determine the doma…
A. The graph of \( y = 6^{x} \) should be shifted vertically up by 4 units. \((-\infty,\infty)\)
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question 9: - let ( f(x) = \frac{2x^2 - 11x + 15}{2x^2 - 5x + 3} ) find…
s: a.) The x-intercepts are \(\boldsymbol{(\frac{5}{2},0)}\) and \(\boldsymbol{(3,0)}\) b.) The y-intercept is \(\boldsymbol{(0,5)}\) c.) The vertical asymptotes are \(\boldsymbol…
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subtract, as shown in the examples. ex. $\frac{4}{5} - \frac{1}{5} = \f…
(1) \(\frac{2}{5}\) (2) \(\frac{1}{5}\) (3) \(\frac{4}{7}\) (4) \(\frac{1}{7}\) (6) \(\frac{7}{9}\) (7) \(\frac{4}{9}\) (8) \(0\)
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a company finds that if it charges x dollars for a cell phone, it can e…
To determine if \( 0\leq x\leq600 \) is appropriate for \( r(x)=x(1000 - 2x) \) (revenue, \( x \) = price) when the company wants to make money: 1. **Model Constraints**: The numb…
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print culture influenced the colonies by sharing ideas in new and power…
A. It spread ideas about independence to many colonists.
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graph the function $f(x) = -7(x + 2)^2 - 1$. plot the vertex. then plot…
Vertex: \((-2, -1)\); Another point: \((-1, -8)\) (plot these on the graph as instructed).
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graph the linear equation, then use the graph to identify the x-interce…
\( m = \boldsymbol{\frac{2}{3}} \), \( b = \boldsymbol{-4} \), \( x \)-intercept \( = \boldsymbol{6} \) ### Problem 11: \( y = -5x + 10 \)
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graph the function $f(x) = 7(x + 3)^2 - 8$. plot the vertex. then plot …
Vertex: \((-3, - 8)\), Another point: \((-2, - 1)\) (and the parabola is graphed with these points, opening upwards)
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instructions 1) work out this problem on one (1) sheet of plain paper. …
The student's error is not applying the chain rule; they failed to multiply the result by the derivative of the upper - limit function $\sin x$ (i.e., $\cos x$) when using the Fun…
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graph the function $f(x) = 8(x - 6)^2 - 1$. plot the vertex. then plot …
The vertex is \((6, -1)\) and another point is \((7, 7)\) (or other valid point, e.g., \( x = 5 \) gives \( f(5) = 8(5 - 6)^2 - 1 = 8 - 1 = 7 \), so \((5, 7)\) is also valid). Whe…
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graph the function f(x) = 8(x + 5)² - 7. plot the vertex. then plot ano…
Vertex: \((-5, -7)\), Another point: \((-4, 1)\) (plot these on the given grid to graph the parabola)
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math is precise; there is only one correct answer. whereas, for me at l…
B. Tan believes that English tests are unfair to nonnative English speakers.
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a company finds that if it charges x dollars for a cell phone, it can e…
A. vertex: \((250, 125000)\) B. left - most intercept: \((0, 0)\) C. right - most intercept: \((500, 0)\)
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part 3: decimals & place value skills: conversions, operations with dec…
\(0.45\)
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question 11 (multiple choice worth 5 points) (03.02r mc) how does the g…
The correct option is: "g(x) is shifted 1 unit to the right and 5 units up." (Assuming this is one of the provided options, likely the first one based on the description.)
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6. multiply or divide. leave your answer as a simplified fraction. a) $…
a) $\boldsymbol{\frac{3}{32}}$ b) $\boldsymbol{\frac{23}{12}}$ (or $1\frac{11}{12}$) c) $\boldsymbol{\frac{3}{22}}$ (assuming the problem for c is $\frac{1}{8} \div \frac{11}{12}$)
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instructions 1) work out this problem on one (1) sheet of plain paper. …
The derivative of \( f(x)=4x - x^{2} \) is \( \boldsymbol{f'(x)=4 - 2x} \). ### Part 2 (Tangent Line):
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function g is represented by the graph. for what input value or values …
-2 and 2 (corresponding to the option: -2 and 2)
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question video examples write a function in any form that would match t…
\(f(x)=\frac{1}{3}(x + 6)^{2}(x - 6)\) (or the expanded form \(\frac{1}{3}x^{3}+2x^{2}-12x - 72\))
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question 4 (multiple choice worth 5 points) (04.02r mc) what value is a…
\(x=-7\) (corresponding to the option with \(x = -7\))
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graph the function f(x) = 4x². plot the vertex. then plot another point…
The vertex is \( (0, 0) \) and another point (e.g., \( (1, 4) \) or \( (-1, 4) \)) can be plotted to graph the parabola \( f(x) = 4x^2 \).
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a particle moves along a straight line. the graph of the particles posi…
A. \( 0 < t < 2 \)
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sketch the graph of the quadratic function and the axis of symmetry. st…
The vertex of the quadratic function \( h(x)=x^2 - 9 \) is \((0, -9)\), and the equation of the axis of symmetry is \( x = 0 \). The graph is a parabola opening upwards with verte…
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4.7\\overline{)9.4}
2
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a school is constructing a rectangular play area against an exterior wa…
\( A = -2w^2 + 120w \)
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11 which function has a point of discontinuity at x = 3 when graphed? a…
D. \(f(x)=\frac{x + 2}{x^{2}-9}\)
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4. which is the graph of $f(x) = x^2 + 4x + 2$?
The graph of \( f(x)=x^2 + 4x + 2 \) is a parabola opening upwards with vertex at \((-2,-2)\) and y - intercept at \((0,2)\). (To identify the specific graph among given options, …
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graph this function: $y = |-2x| + 4$ click to plot the vertex first.
The vertex of the function \( y = |-2x| + 4 \) is at the point \((0, 4)\), so we plot the vertex at \((0, 4)\) first, then use the slope to plot other points and draw the graph.
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find the value of k or h in each of the graphs. see examples 1–3 23. $g…
\( k = 2 \)
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graph this function: $y = |2x|$ click to plot the vertex first.
The vertex of the function \( y = |2x| \) is at \((0,0)\). To complete the graph, plot points like \((1,2)\), \((2,4)\) (for \( x\geq0 \)) and \((-1,2)\), \((-2,4)\) (for \( x < 0…
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what is the equation of the line in point - slope form? use the red poi…
\(y - (-600) = 3(x - (-100))\) so the blanks are \(-600\), \(3\), \(-100\) Wait, but let's recheck the red point. Maybe the red point is at (-100, -600). Let's confirm the slope. …