Calculus Homework Help

1. Volume and Work A container is created by revolving the curve y=x2″ title=”y equals x squared” src=”https://lh4.googleusercontent.com/WJPq_KVsGG8UUgPyELPVR7K5yLLkZfAm8KUf4OYV16GLWt1OZoUFqwyJI2m75-v

1. Volume and Work

A container is created by revolving the curve y=x2″ title=”y equals x squared” src=”https://lh4.googleusercontent.com/WJPq_KVsGG8UUgPyELPVR7K5yLLkZfAm8KUf4OYV16GLWt1OZoUFqwyJI2m75-vuzXeHFl71y2XxS78FB-vUZ25ZRIjc7IY72TZlCGcJ3koGht-qzIBIK8yOi_isQs9-2oB86HxT” width=”54″ height=”23″ style=”margin-left: 0px; margin-top: 0px;”>  from y=0 to y= 9 about the y-axis. 

a. Write an integral that computes V(h), the volume of liquid contained if the container is filled to a height h.

b. How much water does this container hold when it is full?

c. To what height does the water level reach when the volume is half-full?

d. If the container is full of water, how much work does it take to pump all of the water out of the container?  Use the symbols ρ” title=”rho” src=”https://lh4.googleusercontent.com/uSmw8P3W7ReX7fXmU4iju7SdXc1vToia52ydLqgXKn8lWRIIDuOQUe90m5zeVZMp9_Xti3Jda1-g0vz6NcYH2eMMw80F_ijjIWWQuwTIMc8VfhWbovlTJzcYhnHHuFXOxLALoPZw” width=”15″ height=”19″ style=”margin-left: 0px; margin-top: 0px;”> and g in your computations to represent density of water and acceleration of gravity.  If you’d like a number at the end, you can estimateρ=1000kg/m3″ title=”rho equals 1000 k g slash m cubed” src=”https://lh4.googleusercontent.com/dYMhvk_WoQm38ZfbxpoH_zU4yXp0WFBF_ImZvh-Uh6TrbUcvdPEsXYMsyXpfLrdqYEEn4nkh68EU7iCYFIy8e1HpyZjwfA9htUsxpYM6BlErHHvKTecLbjuF2qB0Z_Ra3DOGeCbq” width=”129″ height=”24″ style=”margin-left: 0px; margin-top: 0px;”> and g=10m/s2″ title=”g equals 10 m slash s squared” src=”https://lh6.googleusercontent.com/MPElEv8zC5RIFTj3plVNsWGqbBG86fyQV0vIBAYg1Hn-jVG-JNkxd_Qob8AO2T6K7qnTxXCEST-Rc3CaG04bp4HPUlAtlnzqIb-TfR-c9YuBhabDdqUaD-GGeSTEDMmcDQFBniqZ” width=”96″ height=”24″ style=”margin-left: 0px; margin-top: 0px;”>

e. Your pump breaks down after pumping out half of the volume of water in the tank.  What proportion of the work required to pump all the water out was done?  (Hint: use your answer from above, and think about pumping the water out from the top of the tank down to the remaining water level.)

2. Integration by Parts

Let p(x) be an abstract function defined on the interval [a, b] with the following properties:

p(a) = p(b) = 0

p’’(x) exists for each x in [a,b].

a. Use these properties to show that ∫abp(x)p″(x)dx=−∫ab(p′(x))2dx” title=”the integral from a. to b of p of x p double prime of x equals negative the integral from a. to b of open paren p prime of x close paren squared” src=”https://lh6.googleusercontent.com/6i1MWXbQD5suOEkJC1N8AnKOMRH9Mn2IFuBNTPAi_SpcR4nLUIXirQKd-1v1uC4E7T9BeILcD1HQSqJPElG8f-2gObJCj4QxKCC57GqCaZSy2fg7PEFxVavtND-wYu56ApNjBQbf” width=”336″ height=”56″ style=”margin-left: 0px; margin-top: 0px;”>.  (Hint, integrate the left side by parts and simplify).

As another side note, it will be useful to use the integration by parts formula if the integrals have limits:

∫abf(x)g′(x)dx+∫abf′(x)g(x)dx=f(x)g(x)|ab” title=”the integral from a. to b of f of x g prime of x plus the integral from a. to b of f prime of x g of x equals f of x g of x divides sub a. to the bth power” src=”https://lh3.googleusercontent.com/f-nKprXTAFJZBUufwVMv-_VOGaL-sQ6QclY4lSLgGRRl35e1QjvbMnN7U3tklpJMKdWK4LX9vNlgirQqOiKSSB0r-XjXLB5y8X-yIuY04vyJLbCRrHKO3t4OXhQeAjSyWNLfznpr” width=”455″ height=”56″ style=”margin-left: 0px; margin-top: 0px;”>.    Note that the right side of the equation is evaluated from a to b.

b. In addition to the properties above, suppose p’’ is proportional to p.  In symbols. p’’(x) = Kp(x), for some constant K.  Show that K must be a negative number.

c. We will apply these results to work on a common integral next week.  For now, we just think about functions that satisfy each of the following criteria:

Make up two functions, along with an interval [a, b] for each so that f(a) = f(b) = 0.

Make up two different functions so that f’’(x) = K f(x) for some constant K.

For each of the four functions you wrote down, test each condition.

 
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Calculus Homework Help

Hi, I am posting a question from the topic Optimization in Calculus I. The prerequisite in solving this question : a) Understanding of global maxima and global minima using the first and second deriv

Hi, 

I am posting a question from the topic Optimization in Calculus I. The prerequisite in solving this question :

a) Understanding of global maxima and global minima using the first and second derivative tests.

b) Differentiation rule.

Question : 

A rectangular storage container with an open top is to have  a volume of (10m^3). The length of its base is twice the width. Material for the base costs ($10) per square meter. Material for the side costs ($6) per square meter. Find the cost materials for the cheapest such container.

 
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Calculus Homework Help

Suppose we know the following information about the function f. •the domain of f is (−∞,−1)∪(−1,∞) •f(0) = 0, f(1) =1/2 •f′(−1) is undefined, f′(0) = 0 •f′(x)>0 on (−∞,−1) and (0,∞). ,

Suppose we know the following information about the function f.

•the domain of f is (−∞,−1)∪(−1,∞)

•f(0) = 0,     f(1) =1/2

•f′(−1) is undefined,       f′(0) = 0

•f′(x)>0 on (−∞,−1) and (0,∞).    ,f′(x)<0 on (−1,0)

•f′′(−1) is undefined,   f′′(1) = 0.   

•f′′(x)>0 on (−∞,−1) and (−1,1),       f′′(x)<0 on (1,∞)

•limx→−1f(x) =∞,        limx→±∞f(x) = 1

(1) Find the equation of any vertical asymptotes of f.

(2) On what intervals is f increasing or decreasing?

(3) Find the local maximum and minimum function values of f, and indicate where they occur.

(4) On what intervals isfconcave up or down?

(5) Find all inflection points of f.

(6) Find the equation of the horizontal asymptote of f, or indicate that there is no horizontal asymptote.

(7) Sketch a graph of y=f(x). Label all local max and mins, points of inflection, and asymptotes.

 
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Calculus Homework Help

Select either the minimum or maximum function. Identify a task – personal or professional – that could be modeled mathematically through your chosen function. Explain how the chosen function can be us

Select either the minimum or maximum function. Identify a task – personal or professional – that could be modeled mathematically through your chosen function. Explain how the chosen function can be used in making good decisions. Examples of tasks might be:

Make the largest garden possible using a given amount of fencing.

Configure an airplane to create the least amount of drag for an airplane in flight. 

Be creative!

This question is referring to minima and maxima of derivatives, and is encouraged to detail at least one inflection. 

we are being asked to write three paragraphs detailing the information.

the question i would like to write about is ,   The solar-energy power P (in W) produced by a certain solar system does not rise and fall uniformly during a cloudless day because of the system’s location. An analysis of records shows that P = -0.4512t5 – 45t4 + 350t3 – 1000t22, where t is the time (in h) during which power is produced. Show that, during the solar-power production, the production flattens (inflection) in the middle and then peaks before shutting down. (Hint: The solutions are integral.) …. However, I am open to any creative suggestions. 

Thank you.

 
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Calculus Homework Help

For this I need EVERY step worked out with explinations where possible. EVERY step needs to be justified 100%. If you are unsure about an answer let me know ASAP so that I can get it solved correctly.

For this I need EVERY step worked out with explinations where possible. EVERY step needs to be justified 100%. If you are unsure about an answer let me know ASAP so that I can get it solved correctly. Don’t skip a step. I need to be able to read every character and number so you MUST write clearly. This is Calculus 2. Please read and be sure you can get a 100% answers and Justification for all problems before accepting this.

 
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Calculus Homework Help

1. The production of a chemical satisfies the following differential equation (dP/dt )= ((20)/(1 + 4t)^ 2 ), where t is time in days and P is the amount in moles. (a) Use integration by substitution

1. The production of a chemical satisfies the following differential equation (dP/dt )= ((20)/(1 + 4t)^ 2 ), where t is time in days and P is the amount in moles.

 (a) Use integration by substitution to find the solution, P(t), starting from the initial condition P(0) = 0. 

(b) Sketch the rate of change ( dP dt ) and the solution. 

(c) What happens to P(t) as t → ∞?

3. An outbreak of a novel infectious disease is initially growing at a rate of f(t) = 1.5e 0.12t 

new cases per day (where t is time in days). 

(a) Evaluate a definite integral to find the number of new cases that occur during the first 2 weeks. 

(b) What’s the average number of daily new cases in the first 2 weeks?

 (c) If the rate was initially given by g(t) = 1.5 + 0.12t new cases per day (where t is time in days), how many fewer cases would occur during the first 2 weeks?

 
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