An oil company models the income derived from the continuous production of oil as a continuous income stream using a function f(t), where f(t)=200e^−0.1t, in thousands of dollars per year, where t is in years. Calculate the total income derived from pumping oil after 3 years.   Give your answer in thousands of dollars to the nearest thousand dollars. Do not include commas or the dollar symbol in your answer.

Q: 2. how does the knowledge of differentiability and continuity determine the derivative of functions?

A: A function is said to be differentiable if the derivative of a function exists at all points. The…

Q: Describe geometrically when a function typically does not have a derivative at a point.

A: To describe geometrically when a function typically does not have a derivative at a point.

Q: Evaluate the second derivative at this critical number.

A:

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: How can you sometimes graph the derivative of a function when all you have is a table of the…

A: We can draw the graph of derivative of a function using the values given to us in table of of the…

Q: 2. If the derivative of an accurately determined function is replaced with a finite difference, how…

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: 3. Why first derivative is zero at local maximum and local minimum of function in an open interval?

A: Given, Why the first derivative is zero at the local maximum and a local minimum of function in an…

Q: By using the second derivative test for functions of two variables, find three positive numbers…

A:

Q: f(x)= xe* In(x³)

A: f(x)=xe-xln(x3)According to question we have to calculate the derivative of the function.

Q: f(x) = 6x3 - 9x + 4 +4

A:

Q: Use differentials to estimate the value. estimate =  exact value =

A:

Q: Find the derivative using DELTA METHOD f(x)= 2x-x2

A:

Q: Solve for the second derivative of f(x)=2x-2/x+5

A:

Q: Explain what happens when the derivative of a differentiable function is zero ?

A: To explain when a derivative of differentiable function is zero.

Q: The number of licensed drivers in a country (in millions) can be approximated by the function g(x) =…

A: Here, the given function is: g(x)=178.277x0.065 where x is the number of years and g(x) is the…

Q: Compute the derivative of the function f(x) = 5x² + 3x at the point x = 4. %3D (Give your answer as…

A: We have to find the derivative at that point

Q: Find a function that has x^6 as its derivative without using integral knowlegde.

A: In this question, we need to find a function that has x6 as its derivative.

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Use logarithmic diffenentiation on an alterative method to findthe derivative of the function?

A:

Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: Determine the derivative of 6x log3(x)

A:

Q: Find the derivative by the limit process. f(x) = 10 – x2 %3D

A: We know that the derivative of a function fx is given by:f'x=limh→0fx+h-fxh

Q: se the General Power Rule to find the derivative of the f y = 124x2 + 5

A:

Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

A:

Q: Find the derivative of the function by the limit process. f(x) = 1/x2

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

Q: Find the derivative f(x)= Inlex+9)

A: To find: the derivative of f(x)

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: calculate the 21st derivative of function f(x) = 20-x

A:

Q: show that the function is derivable and that the derivative is continuous.

A: The objective is to show that the given function is derivable and the derivative is continuous.…

Q: Compute the derivative f(x)= cubed root of x + 3/x5

A:

Q: Derive a formula that approximates the second derivative of the function sampled at x = 0, 0.01,…

A: Let us assume that second derivative function  f"x0=Afx0+Bfx0-h+Cfx0+2h can be rewritten as…

Q: Find the derivative of the function f(x)=1/x using limit definition derivative

A: According to the given information it is required to calculate the derivative of the function using…

Q: Find the marginal revenue function.

A:

Q: nd the derivative by the limit process (Gener x) = Vx2 - 4

A: In this question, the concept of the derivative is applied. Derivative The derivative is used to…

Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: find the derivative by using the definition of a deriviative.f(x)= 1/3x+2

A: according to definition of derivative we will evaluate the derivative of f(x)

Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

A:

Q: Find the derivative of the function without using the Quotient Rule. y = -

A:

Q: Suppose that the amount of water pumped from a water well decreases at a continuous rate of 10% per…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: find the derivative by the limit process. f(x)=14-x^2

A: Here we find the derivative by the limit process fx=14-x2

Q: Find the derivative of the function by the limit process. f(x) = 5 − 2/3 x

A:

Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: Estimate the derivative of the function f (x) =: -3 at the point a = 3.

A: The function is given by fx=x3-3 differentiate the above function w.r.t "x" f'x=ddxx3-3…

Q: Find the derivative of the function at Po in the direction of A. txу) - - ху + у, Р,(10, - 2),…

A:

Exponential Growth Model

The relation that represents an exponential function is: