Calculus
Limits, derivatives, optimization, and behavior of functions.
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the palestinian poet mourid barghouti writes that if you want to dispos…
Storytelling reflects power structures in the world.
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8. which sentence correctly shows how the apostrophe is used to form a …
Fred noted it's a poor time to plant spring flowers until after the last frost.
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drawing conclusions from sources what challenges made the lowell mills …
1. faced the risk of being fired or blacklisted 2. had limited negotiating power with corporations 3. had difficulty organizing a union
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comparing american poems: power of words poem 1: the voice of change in…
They create a sense of urgency and progression.
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concept vocabulary why these words? all of the vocabulary words are rel…
1. It helps in using more specific and accurate words to describe feelings. 2. (a) pleased (b) disgusted (c) respected (d) uncomfortable (e) desperate (f) enjoyed
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$\\int_{0}^{8} \frac{dx}{sqrt{1 + x}}$
$4$
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read the excerpt from act i, scene ii of romeo and juliet. benvolio: at…
makes light of Romeo's heartache.
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differentiate the following functions. (a) 4pts. $f(x)=\frac{x^{2}sin(x…
(a) $f^\prime(x)=\frac{(2x\sin(x)+x^{2}\cos(x))(1 + x^{2})-2x\cdot x^{2}\sin(x)}{(1 + x^{2})^{2}}$ (b) $f^\prime(x)=2\sin(3x)\cos(3x)\cdot3\cdot\sin(4x^{5})+\sin^{2}(3x)\cdot\cos(…
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how does the constitution limit the power of the president as commander…
A. It grants power to declare war to Congress
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7 look at the time - distance graph and list the following intervals a.…
\([14,20]\) (the answer may need to be adjusted based on the exact coordinates of the graph, but this is the general interval where the graph shows a decreasing trend)
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the declaration of independence claimed people could change or abolish …
B. Citizens can elect representatives and leaders through voting.
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from last week: how did john locke’s view of the social contract differ…
C. Locke believed in natural rights and that government should protect life, liberty, and property.
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consider the following function. ( f(x) = \frac{2x}{3x - 3} ) which of …
To determine the end - behavior of the function \(f(x)=\frac{x}{3x - 3}\), we can use the method of dividing both the numerator and the denominator by the highest power of \(x\) i…
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elaborating with an explanation should there be term limits on the memb…
- the term length for senators - the term length for members of the House
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elaborating with a definition the idea of clean eating has gained a lot…
B. "clean eating", C. "processed foods", D. "whole foods"
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55. \\lim\\limits_{x\\to 1} \\dfrac{x - 1}{\\sqrt{x} - 1}
2
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53. $limlimits_{h \to 0} \frac{(5 + h)^2 - 25}{h}$
\(10\)
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49. $limlimits_{x \to 4} \frac{\frac{1}{x} - \frac{1}{4}}{x - 4}$
\(-\frac{1}{16}\)
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47. (limlimits_{h \to 0} \frac{sqrt{16 + h} - 4}{h})
$\frac{1}{8}$
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paul has 3600 yards of fencing to enclose a rectangular area. find the …
A rectangle that maximizes the enclosed area has a length of \(\boldsymbol{900}\) yards and a width of \(\boldsymbol{900}\) yards. (Note: The maximum area would be \( A = 900 \tim…
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among all pairs of numbers whose difference is 16, find a pair whose pr…
\(-64\)
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among all pairs of numbers whose difference is 16, find a pair whose pr…
\( 8, - 8 \)
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45. (limlimits_{x \to a} \frac{x - a}{sqrt{x} - sqrt{a}}, a > 0)
$2\sqrt{a}$
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account | date opened | current status | credit limit | balance | remar…
JewelryDotCom ### (b)
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identify whether each value of x is a discontinuity of the function by …
- \( x = -3 \): Asymptote - \( x = -2 \): Asymptote - \( x = 0 \): Hole - \( x = 2 \): Neither - \( x = 3 \): Neither - \( x = 5 \): Neither
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which of the following statements are true of this rational function? c…
The two correct statements are: - There is a removable discontinuity at \( x=-a \). - There is a vertical asymptote at \( x = 0 \).
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1.) $\\lim\\limits_{x \\to -\\infty} \\frac{3x^5 - 6x^4 + 7x^3 - 12x^2 …
$\boldsymbol{\frac{1}{3}}$ ### Problem 2: $\boldsymbol{\lim_{x \to \infty} \frac{-4x^3 - 7x^2 + 8x - 3}{7x^4 - 3x^3 + 5x^2 - 7x}}$
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who later wrote the lord of the rings trilogy, composed a scholarly dis…
1. "hand - forged, fine - webbed mail", "hooped and hasped" (any two alliterations from the text, e.g., also "beaten gold, princely headgear" or "mighty, hand - forged" etc.) 2. "…
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1.) \\lim_{x \\to -\\infty} \\frac{3x^5 - 6x^4 + 7x^3 - 12x^2 + 5x}{9x^…
$\frac{1}{3}$ ### Problem 2: $\lim\limits_{x \to \infty} \frac{-4x^3 - 7x^2 + 8x - 3}{7x^4 - 3x^3 + 5x^2 - 7x}$
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current attempt in progress methane is a greenhouse gas implicated as a…
s: (a) $\frac{w(10)-w(0)}{10-0} = \boldsymbol{14.0}$; $\frac{w(15)-w(10)}{15-10} = \boldsymbol{7.0}$ (b) This tells us that the methane level rises at a slower average rate from t…
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in exercises 37–40, (a) find the points of discontinuity of the integra…
Let's[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]
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view policies current attempt in progress global temperatures may incre…
0.0476
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find the average rate of change of g(x) = 3x³ − 5x² between x = −0.2 an…
-0.2
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current attempt in progress let ( s(t) ) give the number of acres of we…
D. This tells us that between year \( t = 13 \) and \( t = 33 \), the area of wetlands decreased at an average rate of 506 acres per year.
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current attempt in progress let ( g(t) ) give the market value (in $100…
C. The house’s market value increased by $20,000 between years \( t = 0 \) and \( t = 5 \).
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view policies current attempt in progress for the function below, give …
smartphones per dollar
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view policies current attempt in progress for the function below, give …
gallons per mile (or gallons/mile)
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39. $limlimits_{x \to -1} \frac{(2x - 1)^2 - 9}{x + 1}$
\(-12\)
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16. what is the leading cause of death amongst young people? 17. what i…
The leading cause of death among young people (e.g., 15 - 24 years old) is often unintentional injuries, with motor vehicle crashes being a major contributor. Suicide and homicide…
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27. \\(\\int_{a}^{2a} x \\, dx, \\quad a > 0\\) gle sum in sigma in exe…
$\frac{3a^{2}}{2}$
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in exercises evaluate 13. $\\int_{-2}^{4} \\left( \\frac{x}{2} \ ight)$…
To solve[SSE Completed, Client Connection Error][SSE Completed, Client Connection Error][LLM SSE On Failure]
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in exercises 23-28, use areas to 23. \\( \\int_{0}^{b} x \\, dx, \\quad…
\(\frac{1}{2}b^{2}\)
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practice exercises 19–70. evaluating limits find the following limits o…
$\boldsymbol{5}$
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the blue curve shows national health expenditures in billions of dollar…
\$500 billion ### Part (b)
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consider the cost function ( c(x) = 8x^2 + 12x + 25 ) (thousand dollars…
The marginal cost at \( x = 5 \) is 92 thousand dollars per unit. ### Part (b)
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let f(t) be the temperature of a cup of coffee t minutes after it has b…
C. 6 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees. ### Second Question: What does \( f'(6) = -7 \) imply?
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let ( f(t) ) be the temperature of a cup of coffee ( t ) minutes after …
C. 6 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees.
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suppose that f(500) = 8000 and f’(500) = 30. estimate each of the follo…
To solve this problem, we use the linear approximation formula, which is based on the idea that for a function \( f(x) \) that is differentiable at \( x = a \), the value of \( f(…
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congress in a flash a. who does what? read each statement and decide if…
### Part A: Who does what? (Venn Diagram Categorization) To solve this, we recall the roles of the House of Representatives (HoR) and the Senate: - **House of Representatives (Onl…
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a helicopter is rising straight up in the air. its distance from the gr…
\( t = 2 \) seconds ### Part (b)
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15. \\int_{-3}^{3} \\sqrt{9 - x^2} \\, dx \\quad 16. \\int_{\\dots}^{0}…
$\frac{9\pi}{2}$
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33–40 find the absolute maximum and minimum values of f on the set d. 3…
The absolute minimum value of \( f \) on \( D \) is \(-1\) (at the point \((1,0)\)) and the absolute maximum value is \(4\) (at the points \((0,2)\) and \((0, - 2)\)).
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a toy rocket fired straight up into the air has height ( s(t) = 144t - …
The initial velocity is \( \boldsymbol{144} \) feet per second. ### Part (b)
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11. \\(\\int_{-2.1}^{3.4} 0.5 \\, ds\\)
\( 2.75 \)
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an analysis of the daily output of a factory assembly line shows that a…
37
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an object moving in a straight line travels s(t) kilometers in t hours,…
The object's velocity when \( t = 8 \) is \( 150 \) km/h. ### Part (b)
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suppose that ( f(t) = t^2 + 2t - 3 ). (a) what is the average rate of c…
The (instantaneous) rate of change of \( f(t) \) when \( t = 1 \) is \( \boldsymbol{4} \).
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suppose that $f(t) = t^2 + 2t - 3$. (a) what is the average rate of cha…
5
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in exercises 7. \\(\\int_{-2}^{1} 5 \\, dx\\)
\( 15 \)
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suppose that ( f(x) = 3x^2 ). (a) what is the average rate of change of…
### Part (a) - Interval 3 to 3.1 # Explanation: ## Step1: Recall the average rate of change formula The average rate of change of a function \( f(x) \) over the interval \([a, b]\…
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suppose that ( f(x) = 3x^2 ). (a) what is the average rate of change of…
\( 19.5 \)
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suppose that ( f(x) = 3x^2 ). (a) what is the average rate of change of…
21
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what is drawn with gerrymandering? ○ state boundaries ○ city limits ○ c…
D. political districts to benefit a party
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41–48 ■ find the sum. 41. \\( \\sum_{k=1}^4 k \\) 42. \\( \\sum_{k=1}^4…
\( 10 \) ### Problem 42: $\sum_{k=1}^{4} k^2$
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what major constitutional principle was upheld by the supreme court in …
c. Students have rights at school ### Second Question:
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is it true that a continuous function that is never zero on an interval…
Yes. By the Intermediate Value Theorem, if a function changed sign, its value was zero at some point.
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for what values of a is the following function continuous at every x? f…
\( a = -3, 4 \)
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17. please list the following parking restrictions. 1. 2. 3. 4. 5.
1. No parking in fire lanes 2. No parking in handicapped zones (without permit) 3. Time - limited parking (e.g., 2 - hour parking) 4. No parking during street sweeping hours 5. No…
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suppose the revenue from producing (and selling) x units of a product i…
100, 350
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for what value of a is the following function continuous at every x? $f…
A. \(a=\frac{1}{3}\)
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at what points is the following function continuous? $f(x) = \\begin{ca…
\((-\infty, \infty)\)
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1. ( e^{sin(cos x)} = y )
The derivative of \( y = e^{\sin(\cos x)} \) with respect to \( x \) is \( -e^{\sin(\cos x)}\cos(\cos x)\sin x \)
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find the derivative: 3. ( y = 4x^3 + 6sqrt{x} - \frac{3}{x^2} + dots ) …
\( y' = 12x^{2}+\frac{3}{\sqrt{x}}+\frac{6}{x^{3}} \)
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at what points is the function ( y = \frac{sin x}{6x - 6} ) continuous?…
\( (-\infty, 1) \cup (1, \infty) \)
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1. what document was promoted by the anti-federalists and protects the …
Bill of Rights ### Question 2
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a characteristic of free enterprise is private ownership. what is it? a…
Strengthens: Promotes economic freedom, growth, and innovation aligned with democratic values. Challenges: Concentrates economic/political power, creates inequality, and strains d…
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at what points is the given function f(x) continuous? $f(x)=\\frac{6}{x…
\((-\infty, 4) \cup (4, \infty)\)
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use the graph to answer the question about discontinuity. determine the…
A. There is a discontinuity that can be removed by defining \( f(3)=0 \)
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7. y = (sec x + tan x)^5
The derivative of \( y = (\sec x+\tan x)^{5} \) is \( \boldsymbol{5\sec x(\sec x + \tan x)^{5}} \) (if the problem was to find the derivative. If the problem was different, for ex…
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what is the name of the system in which each branch of the u.s. governm…
B. checks and balances
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use the following function and its graph to answer parts a through d be…
\( \lim_{x \to 2^-} f(x)=\boxed{3} \) (so the correct choice is A with the answer 3)
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y = \\sqrt5{x^4 + \\cos 2x}
The derivative of \( y = \sqrt[5]{x^{4}+\cos 2x} \) is \( \frac{4x^{3}-2\sin(2x)}{5\sqrt[5]{(x^{4}+\cos 2x)^{4}}} \)
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use the following function and its graph to answer parts a through d be…
A. \( \lim_{x \to 2^+} f(x)=\boxed{3} \)
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use the following function and its graph to answer parts a through d be…
C. Yes, \(\lim\limits_{x\to3}f(x)\) exists and equals \(2\).
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use the following function and its graph to answer parts a through d be…
A. \( f(3)=\boldsymbol{3} \) (Simplify your answer.)
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name: ____________________ date: 9/5/18/23 period______ teacher: bingha…
- Which branch is being limited: Executive branch (the President, as executive orders come from the executive branch). - Which branch has this checking power: Judicial branch (the…
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use the following function and its graph to answer parts a through d be…
\( \lim\limits_{x\to 3^+} f(x) = 2 \)
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name: ____________ date: 9-9-2025 period: ____ teacher: bingham, hasseb…
The executive branch (president) is being limited. The judicial branch (Supreme Court) has the checking power (judicial review) to declare executive actions unconstitutional. ### …
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use the relation \\(\\lim_{\\theta \\to 0} \\frac{\\sin \\theta}{\\thet…
\(\frac{1}{11}\)
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what is the connection between ratification and the bill of rights? ale…
B. Five states ratified on the condition that amendments would be added soon after the Constitution went into effect.
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2. give the derivatives of the following functions. for this problem, w…
\( 3e^{2x}(2\tan x + \sec^2 x) \) (or equivalently \( 6e^{2x}\tan x + 3e^{2x}\sec^2 x \))
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use the relation \\(\\lim_{\\theta \\to 0} \\frac{\\sin \\theta}{\\thet…
A. \(\lim\limits_{\theta ightarrow0}\frac{\sin\theta}{\sin(90)}=\boxed{0}\)
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question 39 2 pts which of the following is true of working memory? wor…
A. Working memory capacity is strongly related to cognitive aptitudes, such as intelligence.
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find the limit using \\(\\lim\\limits_{\\theta \\to 0} \\dfrac{\\sin \\…
A. \(\lim\limits_{x ightarrow0}\frac{x\csc 10x}{\cos 8x}=\frac{1}{10}\)
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completar unlimited attempts left due september 11th 11:59 pm fill in t…
se enoj (Note: The "á" might be a typo; correct conjugation for ellos is "se enojan") ### 2.
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use the relation (lim_{\theta \to 0} \frac{sin \theta}{\theta} = 1) to …
A. \( \lim\limits_{\theta \to 0} \dfrac{6\sin \sqrt{4}\theta}{\sqrt{4}\theta}=\boxed{6} \)
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3. $cos x^4 = f(g(x))$ where $f(x) = $ , and $g(x) = $ .
$f(x)=\cos(x)$, $g(x)=x^4$
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completar unlimited attempts left due september 11th 11:59 pm fill in t…
se enojan ### 2.
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which of the following is not permitted in a roundabout? changing lanes…
Changing lanes
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1. (cos^4(x) = f(g(x))) where (f(x) = square), and (g(x) = square).
\(f(x) = x^4\), \(g(x)=\cos(x)\)