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 =... more

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

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.

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... more

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?

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?

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!

Solve Using Table of Integrals

∫(xe^x)dx=

Simplify: (6a-4b)/5-(b+7a)/3-2

Simplify:3-(2x-y)/4+(x+4y)/12

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... more

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.

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... more

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... more

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.... more

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... more

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.

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... more

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... more

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... more

calc help please

if 8x-11 <= f(x) <= 2x^2 -3 for all xE [0,4], then limx--2 f(x)=

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?

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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