微积分
极限、导数、最优化与函数性质。
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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 it has b…
C. 6 minutes after the coffee has been poured, the temperature of the cup of coffee is 130 degrees. ### Second Question (Interpret \( f'(6) = -7 \)):
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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).
\(f(x) = x^4\), \(g(x)=\cos(x)\)
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a. graph ( f(x) = \begin{cases} 4 - x^2, & x eq -2 \\ 7, & x = -2 end{c…
### Part a: To determine the correct graph, we analyze the function \( f(x)=\begin{cases}4 - x^2, & x eq - 2\\7, & x = - 2\end{cases}\) - The function \(y = 4-x^{2}\) is a downwa…
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use the following function and its graph to answer parts a through d be…
A. \( \lim\limits_{x \to 3^-} f(x) = \boldsymbol{2} \)
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the following three functions look very similar, but define very differ…
(for Problem 1): $f(x) = x^4$, $g(x) = \cos(x)$ ### Problem 2: $\boldsymbol{\cos(\cos(x)) = f(g(x))}$
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use the following function and its graph to answer parts a through d be…
A. \( \lim\limits_{x\to 3^+} f(x) = 2 \)
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la fiesta elegante unlimited attempts left due september 11th 11:59 pm …
lavarás ### Question 2
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why did thomas jefferson object to letting the national government issu…
C. Giving Congress any power not explicitly granted by the Constitution will remove all limits on its power.
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true or false: $\\lim\\limits_{x \\to 0^-} f(x) = \\lim\\limits_{x \\to…
True (the option with "True" for the question "True or false: $\lim\limits_{x\to 0} f(x) = 0$")
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use the graph below to determine whether the statements about the funct…
True
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use the graph below to determine whether the statements about the funct…
True ### Second Statement: $\boldsymbol{\lim_{x \to 0^-} f(x) = 3}$
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the three-fifths compromise established which of the following? a two-h…
only part of the slave population counting toward representation
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use the graph below to determine whether the statements about the funct…
s: - For $\lim_{x \to -3^+} f(x) = 9$: True - For $\lim_{x \to 0^-} f(x) = 3$: False
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what did the great compromise establish? ○ a weak executive branch of t…
D. a two - house (bicameral) federal legislature made up of an upper and a lower house (assuming the last option is labeled D, if the original labels were different, adjust the la…
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chapter 1 & 2 review question 34 of 34 (1 point) | question attempt: 1 …
- **Whole numbers (and Integers, Rational numbers)**: 14, 0 - **Integers (but not Whole numbers, and Rational numbers)**: - 28, - 20 - **Rational numbers (but not Integers)**: - 9…
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1. what is a short story?
A short story is a brief work of prose fiction, typically focusing on a single plot, a limited number of characters, and a concise narrative to convey a theme, idea, or event, oft…
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use the graph below to determine whether the statements about the funct…
True
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autoevaluación unlimited attempts left due september 11th 11:59 pm 1 ar…
el, la ### 2. For "comunidades"
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the english bill of rights created _______. a limited monarchy b absolu…
A. limited monarchy ### Second Question: Which of these was NOT a part of the English Bill of Rights?
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correspondencias unlimited attempts left due sep select the definite ar…
el ### 2. For "palabras"
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find the general derivative ( f(x) ) for ( f(x) = \frac{12}{x+3} ) usin…
\( f^{\prime}(x)=-\frac{12}{(x + 3)^2} \)
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which point is a relative minimum?
C
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why was the magna carta important for the development of democracy? a i…
D. The Magna Carta limited the King’s power and prevented absolutism from taking hold in England.
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how did the english bill of rights change the government structure of e…
D. It limited the monarch’s power to be shared with Parliament and the people.
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what was the purpose of the english bill of rights? a to reinstate king…
D. To limit the power of the British monarch
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in the republic of costa rica, each branch of government has different …
To solve this, we analyze the passage: ### 1. First blank: "In Costa Rica, power is held by ____ of government." The passage describes three branches (executive, legislative, judi…
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ma 241 si: sections 3.1 and 3.2 - tangent lines and the derivative at a…
### Part 1: Conceptual Fill - ins #### Explanation: The general formula for the derivative of a function \(y = f(x)\) with respect to \(x\) is given by the limit definition: \(f^{…
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7–13. assume \\(\\lim\\limits_{x \\to 1} f(x) = 8\\), \\(\\lim\\limits_…
$32$ (using Constant Multiple Law) ### Problem 8: $\lim\limits_{x\to 1}\frac{f(x)}{h(x)}$
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there are many types of governments. some governments are democratic. i…
A. Citizens have a choice about who governs them, B. Government officials must operate within the law
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6. evaluate the following limits using calculus methods and draw conclu…
s: b) \(\boldsymbol{+\infty}\) c) \(\boldsymbol{+\infty}\) d) \(\boldsymbol{6}\) e) \(\boldsymbol{\frac{3}{5}}\) f) \(\boldsymbol{+\infty}\) g) \(\boldsymbol{0}\)
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what were progressives most concerned about in capitalist society? maxi…
Addressing social problems
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question 15 (1 point) listen nadda believes the following: \it is wrong…
c) relative