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Calculus Math

12/17/23

partial fractions

find the volume generated by revolving the area bounded by y = (1/x^3+7x^2+10x), x=4, x=8 and y = 0 about the y-axis.

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Calculus

12/16/23

Use L’Hopitals Rule to evaluate the following limits lim (ln 𝑥)^𝑥−1 𝑥→1

Use L’Hopitals Rule to evaluate the following limits lim 𝑥→1(ln 𝑥)𝑥−1

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Calculus

12/16/23

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom.

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom. Find the dimensions of the poster with the... more

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Calculus

12/16/23

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom.

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom. Find the dimensions of the poster with the... more

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Calculus

12/16/23

Let 𝑓(𝑥) = 𝑝𝑥^2 + 𝑞𝑥 + 𝑟 . Prove that for any interval [𝑎 , 𝑏] the value 𝑐 guaranteed by the mean value theorem is the midpoint of the interval.

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Calculus

12/16/23

Find 𝑑^2𝑥/𝑑𝑥^2 by implicit differentiation 𝑦^2 + 𝑥^2 = 𝑒 √sin 𝑥𝑦+ln 𝑥𝑦

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Calculus

12/16/23

Integral S Calculus 3 Question

Evaluate ∬SF⋅dS where F=−xi+2yj−zk and S is the portion of y=3x2+3z2 that lies behind y=6 oriented in the positive y-axis direction.Thank you in advance!

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Calculus Math Business

12/15/23

find a demand function d(q) , where q is the quantity/number of the spectators. (assume d(q) is linear)

a baseball team plays in a stadium that holds 72000 spectators. with the ticket price at $8 the average attendance has been 29000. when the price dropped to $4, the average attendance rose to... more

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Calculus

12/15/23

Determine the absolute maximum and the absolute minimum value of th

Determine the absolute maximum and the absolute minimum value of the functionf (x) = sin^2 x X-SQRT2cos xon the interval (0,3pi/2)

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Calculus

12/15/23

DETERMINE SECOND DERIVATIVES

Determine y’’ given: y = 3^ax + sin (bx) where a, b E R are constants.

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Calculus

12/15/23

I think this is related rates please help

your distance from a place = the speed you’re going in mph. Your 100 miles away at 1pm, how fast are you going at 2pm

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Calculus Math

12/14/23

Which of these physical settings make sense for the object in question 1, whose position is given by a(t) = -3 cos(t)?

A car driving from San Diego to Los Angeles. B. An ant walking at a steady pace from the tip of a propeller toward the hub. C. A skydiver falling from a plane, before she opens her parachute. D.... more

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Calculus Math

12/14/23

How fast is the water level rising when the water level is 5m from the bottom of the tank?

A hemispherical water tank with a radius of 10 m is filled from an inflow pipe at a rate of 3 m^3/min. How fast is the water level rising when the water level is 5m from the bottom of the tank?... more

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Calculus

12/14/23

Calculus 3 Integral

Evaluate ∬SF⋅dS where F=−xi+2yj−zk and S is the portion of y=3x2+3z2 that lies behind y=6 oriented in the positive y-axis direction

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Calculus

12/14/23

Length in cm for fish

The length (in cm) of a particular species of fish at time t (in months) is given by:L(t)= 34-32(k^t)k a constant.(a) If L (4) = 10, find the value of k for this particular species of... more

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Calculus

12/14/23

Equation of the tangent

Determine the equation of the tangent to the curve: cos (x y) = ye^x -pi/2at the point (x; y) = (0,pi/2) you will need to use implicit differentiation.

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Calculus

12/14/23

Equation of the tangent

Determine the equation of the tangent to the curve: cos (x y) = ye^x -pi/2at the point (x; y) = (0,pi/2) you will need to use implicit differentiation.

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Calculus

12/14/23

Object moving position

A moving object’s position, relative to some initial reference point, is given in metres by: s (t) = (t -4)^2 -6, where t is measured in seconds.(a) Find the average velocity of the object over the... more

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Calculus

12/14/23

Marginal Profit

Suppose that the marginal profit function for a company is P'(x)=120+34x-3x^2 at a production level of x units.Find the extra profit earned from the sale of 6 additional units if 8 units have... more

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Calculus

12/14/23

True or False. lim x→a f(x) = L means that if x1 is closer to a than x2 is, then f(x1) will be closer to L than f(x2) is.

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Calculus

12/14/23

True or False. If f(x) = (x^2−16) / (x−4) and g(x) = x + 4, then we can say the functions f and g?

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Calculus Precalculus

12/14/23

The angle of elevation of the sun is decreasing at 1/4 rad/h. How fast is the shadow cast by a building of height 30 m lengthening, when the angle of elevation of the sun is π/4?

The angle of elevation of the sun is decreasing at 1/4 rad/h. How fast is the shadow cast by a building of height 30 m lengthening, when the angle of elevation of the sun is π/4? Leave your answer... more

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Calculus Math Precalculus

12/14/23

How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?

A street light is at the top of a 14 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 4 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 35... more

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Calculus Math Precalculus

12/14/23

The radius of a sphere is increasing at a rate of 5 meters per hour. When the radius is 12 meters, then how fast is the VOLUME changing?

The radius of a sphere is increasing at a rate of 5 meters per hour. When the radius is 12 meters, then how fast is the VOLUME changing?Note: Volume of a sphere = (4/3) ⋅ π ⋅ (radius)3The rate of... more

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Calculus Math Precalculus

12/14/23

A circle is inside a square. The radius of a circle is increasing at a rate of 4 meters per day and the sides of the square are increasing at a rate of 3 meters per day.

A circle is inside a square.The radius of a circle is increasing at a rate of4 meters per day and the sides of the squareare increasing at a rate of 3 meters per day.When the radius is 3 meters,and... more

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partial fractions

Use L’Hopitals Rule to evaluate the following limits lim (ln 𝑥)^𝑥−1 𝑥→1

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom.

A rectangular poster is to have an area of 100 square inches with a 1-inch margin on the right and left sides and a 2-inch margin at the top and bottom.

Let 𝑓(𝑥) = 𝑝𝑥^2 + 𝑞𝑥 + 𝑟 . Prove that for any interval [𝑎 , 𝑏] the value 𝑐 guaranteed by the mean value theorem is the midpoint of the interval.

Find 𝑑^2𝑥/𝑑𝑥^2 by implicit differentiation 𝑦^2 + 𝑥^2 = 𝑒 √sin 𝑥𝑦+ln 𝑥𝑦

Integral S Calculus 3 Question

find a demand function d(q) , where q is the quantity/number of the spectators. (assume d(q) is linear)

Determine the absolute maximum and the absolute minimum value of th

DETERMINE SECOND DERIVATIVES

I think this is related rates please help

Which of these physical settings make sense for the object in question 1, whose position is given by a(t) = -3 cos(t)?

How fast is the water level rising when the water level is 5m from the bottom of the tank?

Calculus 3 Integral

Length in cm for fish

Equation of the tangent

Equation of the tangent

Object moving position

Marginal Profit

True or False. lim x→a f(x) = L means that if x1 is closer to a than x2 is, then f(x1) will be closer to L than f(x2) is.

True or False. If f(x) = (x^2−16) / (x−4) and g(x) = x + 4, then we can say the functions f and g?

The angle of elevation of the sun is decreasing at 1/4 rad/h. How fast is the shadow cast by a building of height 30 m lengthening, when the angle of elevation of the sun is π/4?

How fast is the tip of her shadow moving when she is 35 ft from the base of the pole?

The radius of a sphere is increasing at a rate of 5 meters per hour. When the radius is 12 meters, then how fast is the VOLUME changing?

A circle is inside a square. The radius of a circle is increasing at a rate of 4 meters per day and the sides of the square are increasing at a rate of 3 meters per day.

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