5,781 Answered Questions for the topic calculus

11h

#### I am so tilted! Please help me! (Multivariate Calculus about finding Extrema!)

Good day!Show that f(x,y) = 1 - x^4 - y^4 has a relative maximum, even though D(Discriminant) in the theorem is 0.JUST HOW!!!!!! I AM TILTED AF PLEASE HELP ME!I will show my working so far:fx =...
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21h

#### sketch the graph of a function that satisfies the given conditions:

f(0)=0f is continuous and evenf'(x)=2x if 0<x<1f'(x)=-1 if 1<x<3f'(x)=1 if x>3

1d

#### The linear density of a rod of length 4 m is given by ρ(x) = 10 + 5sqrt(x) measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

The linear density of a rod of length 4 m is given by ρ(x) = 10 + 5sqrt(x) measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

1d

#### Cedar plank math question

Suppose you have a cedar plank of length 36 inches and width 3 inches. For the purpose of this problem, suppose the thickness of wood is negligible.
If you use this plank for the sides of the...
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1d

#### Find the area between f(x)=cosx and g(x)=-sinx on [0,pi/2]

I got these wavy curves near the x-axis but my trig is weak. I know I need to stay in the 1st quadrant since it's on [0,pi/2]. I can't find any videos or in step details online so far. Any help?

1d

#### Find the average value of y=sinx on [0,pi]

I have the equation 1/pi ∫ [0,pi]sinx dy. Am i setting up this equation correctly?

1d

#### Find the average value of f(x)=x^3 on [-1,1]

I understand that this is the formula 1/(b-a)∫ f(x) dx but im having trouble plugging in the values correctly. Any light on the subject would be much appreciated!

1d

#### Consider the Function

Consider the function f(x)=x3-9x2.a. Find a formula for f'(x).b. Use your answer to part (a) to find any critical points of f.c. Use either the first or second derivative test to classify any...
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1d

#### Elasticity of demand

The elasticity of demand of milk is 0.49. If the price of milk increases 40%, what change in demand would you expect? Be specific about both the direction of the change and how much it changes.

1d

#### Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5s.

Breathing is cyclic and a full respiratory cycle from the beginning of inhalation to the end of exhalation takes about 5 s. The maximum rate of air flow into the lungs is about 0.5 L/s. This...
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1d

#### A bacteria population starts with 500 bacteria and grows at a rate of r(t) = (450.266)e^1.12567t bacteria per hour.

A bacteria population starts with 500 bacteria and grows at a rate of r(t) = (450.266)e1.12567t bacteria per hour. How many bacteria will there be after three hours? (Round your answer to the...
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1d

#### The area of the region that lies to the right of the y-axis and to the left of the parabola x = 4y − y2

The area of the region that lies to the right of the y-axis and to the left of the parabola x = 4y − y2 (the shaded region in the figure) is given by the integral, integral sign 0 to 4 (4y-y^2)dy....
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1d

#### The marginal cost of manufacturing x yards of a certain fabric is C'(x) = 3 − 0.01x + 0.000009x2

The marginal cost of manufacturing x yards of a certain fabric is C^'(x) = 3 − 0.01x + 0.000009x2 (in dollars per yard). Find the increase in cost if the production level is raised from 2000 yards...
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1d

#### The linear density of a rod of length 4 m is given by ρ(x) = 10 + 5 sqrt(x) measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

The linear density of a rod of length 4 m is given by ρ(x) = 10 + 5sqrt(x)
measured in kilograms per meter, where x is measured in meters from one end of the rod. Find the total mass of the rod.

1d

#### The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line. a(t) = t + 8, v(0) = 7, 0 ≤ t ≤ 10

The acceleration function (in m/s2) and the initial velocity are given for a particle moving along a line.a(t) = t + 8, v(0) = 7, 0 ≤ t ≤ 10(a) Find the velocity at time t.(b) Find the...
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1d

#### The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t − 8, 0 ≤ t ≤ 3

The velocity function (in meters per second) is given for a particle moving along a line.v(t) = 5t − 8, 0 ≤ t ≤ 3(a) Find the displacement.(b) Find the distance traveled by the particle during...
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1d

#### Calculus Question

Given the revenue and cost functions R=32x-0.8x^2 and C=5x+12, where x is the daily production, find the rate of change of profit with respect to time when 15 units are produced and the rate of...
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1d

#### A 20 ft piece of wire is cut into 2 pieces. One piece is bent into a square and the other is bent into an equilateral triangle [cont. in description]

Where should the wire be cut so that the total area enclosed by both is minimum and maximum?

1d

#### sketch the graph of a function that satisfies the given conditions: [cont in description]

f(0)=0f is continuous and even f'(x)=2x if 0<x<1f'(x)=-1 if 1<x<3f'(x)=1 if x>3

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