12.Determine analytically, showing all work, all values of x (if any) at which the the func on f(x)

1. Find analytically the equation of the line that is tangent to g(x)=sqrt（-x-3 ）and parallel to the line y=-1/2x+2. Use the limit definition of the derivative and find the point of tangency by hand, showing all work. Verify your results by sketching

1. The position of an object moving along a line is given by the function s(t) = t^2-2t .

1. The position of an object moving along a line is given by the function s(t) = t^2-2t . What is the average velocity over the interval [0, 2] ? 2. The position of an object moving along a line is s(t) = t^2-2t . Approximate the instantane

Determine an equation of the line that is perpendicular to the tangent to the graph of f(x)=1/( x ) at x=2 and that intersects it at the point of tangency.

Applying Newton's law of cooling and differential equations

Suppose we place a 90 °C cup of coffee into a 20 °C room. If the coffee is in a Styrofoam cup for which k≈−0.05, what is the temperature of the coffee as a function of time?

Differential equations with exponential growth and decay

The rate of change of the amount of morphine in the human bloodstream is proportional to the amount of morphine present. If initially there is 0.4 mg of morphine in the bloodstream, and only 0.2 mg remains after 3 hours, find an equation for the amou

Differential equations with exponential growth and decay

Suppose that a rumour spreads according to dP/dt=1.1P. If 3 people know the rumour initially, how many people will know the rumour as a function of time?

How to setup and solve differential equation problems

A certain small country has $10000 million in paper currency in circulation and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever ol

How to setup and solve differential equation problems

A 15 000 ft^3 room has 20 ppm smoke. Fresh air enters at a rate of 1200 ft^3/min and forces the smoky air out. What is the smoke content as a function of time?

How to setup and solve differential equation problems

A tank contains 10 L of water with 4 g/( L ) of dissolved salt. Water containing 2 g/( L ) of salt enters the tank at a rate of 7 L/( min ). The solution is kept thoroghly mixed and drains from the tank at the same rate.

How do I setup and solve differential equation problems

Suppose we have 7000 L of water with 50 kg of salt in it. If we add pure water at a rate Of 2 L/min and add water containing 0.6 kg/L of salt at a rate of 9 L/min, and we know that water flows out at a rate of 11 L/min, then what is the salt content

Write an equation of a curve for a differential system

The slope of a curve at each point is one-tenth the product of the ordinate and the square of the abscissa, and the curve passes through the point (2, 3).