25,270 Answered Questions for the topic calculus

03/08/24

derivative and antiderivative of ln(2x)
Alright, if I were to find dy/dx of ln(2x) I'd get 1/2x.2, so 2/2x and that can be simplified as 1/x.However, if I were to integrate 1/x to attempt to infer my original function, I'd get ln(x) +... more
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Calculus

03/08/24

Trigonometric substitution

Evaluate the integral:Integral of (-3x^3) / (sqrt((x^2) + 9) dx, x = 3tan(theta)
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Calculus

03/08/24

Calculus 2: Volumes and Volumes by Cyl. Shells HW problem.
Problem:Graph the following enclosed region:y=-x^2+11x , y=0, x=0State the method that be used to find the volume of the solid created by rotating the region about the following axis of rotation:a)... more
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Calculus

03/08/24

Use mean value theorem
πΆπ‘œπ‘›π‘ π‘–π‘‘π‘’π‘Ÿ π‘‘β„Žπ‘’ π‘“π‘œπ‘™π‘™π‘œπ‘€π‘–π‘›π‘” π‘“π‘’π‘›π‘π‘‘π‘–π‘œπ‘› π‘€β„Žπ‘–π‘β„Ž 𝑖𝑠 π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘‘π‘–π‘Žπ‘π‘™π‘’ π‘“π‘œπ‘Ÿ π‘Žπ‘™π‘™ π‘₯: 𝑓(π‘₯) = { π‘₯ 3 + 2π‘₯ 2 βˆ’ 4π‘₯ + 2, 𝑖𝑓 π‘₯ ≀ 1 3π‘₯ βˆ’ 2, 𝑖𝑓 π‘₯ > 1 πΉπ‘œπ‘Ÿ π‘‘β„Žπ‘’ π‘–π‘›π‘‘π‘’π‘Ÿπ‘£π‘Žπ‘™ βˆ’ 4 ≀ π‘₯ ≀ 2, 𝑓𝑖𝑛𝑑 π‘Žπ‘™π‘™ π‘£π‘Žπ‘™π‘’π‘’π‘  π‘œπ‘“ 𝑐 π‘‘β„Žπ‘Žπ‘‘ π‘ π‘Žπ‘‘π‘–π‘ π‘“π‘¦... more
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Calculus

03/08/24

Prove the following equation

π‘ˆπ‘ π‘’ π‘‘β„Žπ‘’ π‘‘π‘’π‘“π‘–π‘›π‘–π‘‘π‘–π‘œπ‘› π‘‘π‘œ π‘π‘Ÿπ‘œπ‘£π‘’ π‘‘β„Žπ‘Žπ‘‘ limπ‘›β†’βˆ’51(π‘₯+5)6 = ∞
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Calculus

03/08/24

Use implicit derivative to find y'
π‘ˆπ‘ π‘’ π‘–π‘šπ‘π‘™π‘–π‘π‘–π‘‘ π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘‘π‘–π‘Žπ‘‘π‘–π‘œπ‘› π‘‘π‘œ 𝑓𝑖𝑛𝑑 𝑦 β€² 𝑖𝑛 π‘‘β„Žπ‘’ π‘“π‘œπ‘™π‘™π‘œπ‘€π‘–π‘›π‘”: 3π‘₯𝑦 2 + πΆπ‘œπ‘ (𝑦 2 + 𝑆𝑒𝑐 π‘₯) = ln (π‘₯ 2 + 𝑦)
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Calculus

03/08/24

Find the domain
𝐿𝑒𝑑 𝑓(π‘₯) = {3π‘₯2𝑆𝑖𝑛 1π‘₯𝑖𝑓 π‘₯ β‰  00 𝑖𝑓 π‘₯ = 0 (a) 𝐹𝑖𝑛𝑑 π‘‘β„Žπ‘’ π‘‘π‘œπ‘šπ‘Žπ‘–π‘› 𝐷𝑓 π‘œπ‘“ 𝑓(π‘₯).
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Calculus

03/08/24

f(t)=t^3-12t^2+36t
(e) Find the total distance traveled during the firstΒ 7Β s.
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Calculus

03/08/24

The top of a 13 foot ladder, leaning against a vertical wall, is slipping down the wall at the rate of 4 feet per second.

How fast is the bottom of the ladder sliding along the ground when the bottom of the ladder is 9 feet away from the base of the wall? (Round your answer to four decimal places. Be sure to choose... more
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Calculus

03/08/24

Let l be the length of a diagonal of a rectangle whose sides have lengths x and y, and assume that x and y vary with time.
if x increases at a constant rate of 1/6ft/s and y decreases at a constant rate of 1/8 ft/s, how fast is the size of the diagonal changing whenΒ xΒ =Β 4Β ftΒ andΒ yΒ =Β 4Β ft?Β (Round your answer to four... more
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Calculus

03/08/24

max and min help?
Within the interval (-0.93,4.77), for what value of x does f(x) take on a minimum iff(x)=3.2sin(1.1x)+5.3cos(1.1x)Minimum value of f(x) occurs at x=What is the value of f(x) at this value of x... more
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Calculus

03/07/24

Find an equation of the tangent line to the curve at the given point.

Find an equation of the tangent line to the curve at the given point.f(x) =Β 3x2Β βˆ’Β x3,Β Β (1,Β 2) ο»ΏyΒ =Β Β 
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Calculus

03/07/24

Find equations of the tangent line and normal line to the curve at the given point
Find equations of the tangent line and normal line to the curve at the given point.yΒ =Β x4Β +Β 5ex,Β Β (0,Β 5)tangent line y=Β normal line y=Β 
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Calculus

03/07/24

Find an equation of the tangent line to the curve at the given point
Find an equation of the tangent line to the curve at the given point.yΒ =Β 2x3Β βˆ’Β x2Β +Β 7,Β Β (2,Β 19)
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Calculus

03/07/24

Evaluate the indefinite integral. (Use C for the constant of integration.)
x rad 8-x^2 dx
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Calculus

03/07/24

Evaluate the integral by making the given substitution. (Use C for the constant of integration.)
x^2 rad x^3+5 dx, u=x^3 + 5
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Calculus

03/07/24

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
g(s) =8Β --)S (t-t^4)^9 dtg'(s) = ?
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Calculus

03/07/24

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.
0Β --)X Rad t^3 + t^5 dt
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Calculus

03/07/24

Find the point on the line y = 3x + 2 that is closest to the origin.
(x, y) =
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Calculus

03/07/24

Find the point on the line y = 3x + 2 that is closest to the origin.
(x, y) =
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Calculus

03/07/24

A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used.
side of base = ___cmheight = ____cm
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Calculus

03/07/24

A model used for the yield Y of an agricultural crop as a function of the nitrogen level N in the soil (measured in appropriate units) is
Y = KN/(9+N^2) whereΒ kΒ is a positive constant. What nitrogen level gives the best yield? N=
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Calculus Python

03/07/24

Consider the curve given by x^2 + 2x + 3y^2 = 8:
(a) Find dy/dx .(b) Find the points (x and y coordinates) where the graph of the equation has a horizontaltangent line.(c) Find the points (x and y coordinates) where the graph of the equation has... more
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Calculus Python

03/06/24

given the equation x^3-y^3=12xy:
a) find dy/dxb) Find the points (x and y coordinates) where the graph of the equation has a horizontal tangent line.(c) Find the points (x and y coordinates) where the graph of the equation has a... more
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Calculus

03/06/24

Working with Tangent and sin and velocity and curves.
LetΒ β„Ž(x)=tan(2x+7). Thenβ„Žβ€²(1)Β isΒ Β Β andΒ β„Žβ€²β€²(1)Β isΒ 2.Find the derivative of:Β -3e^-5x cos(-5x).Now, find the equation of theΒ tangent lineΒ to the curve atΒ x=0. Write your answer in mx+bΒ format.y=3.A... more
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