The rate of change of the value of goods exported from a country between 1990 and 2001 can be modeled as E'(t) = -1.662t² + 16.474t + 7.632 billion dollars per year and the rate of change of the value of good imported into the country during those years can be modeled as I'(t) = 4.916t + 40.861 billion dollars per year where t is the number of years since 1990. (a) Calculate the difference between the accumulated value of imports and the accumulated value of exports from the end of 1990 through 2001. (Round your answer to three decimal places.) $ billion (b) Is the answer from part (a) the same as the area of the region(s) between the graphs of E' and I'? Yes No Explain. Since the graphs ---Select--- , the answer to part (a) ---Select--- the area of the region(s) between the curves.

Q: 1. When an object is in free fall near the surface of the Earth, the only force acting on it is the…

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Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: Find the derivative: y = ln² (3x + 1) O y' = O O O y' = y' = y = 2 ln(3x + 1) (3x + 1) 6 (3x + 1) 3…

A: Consider the function y=ln2(3x+1). The objective is to find the derivative of the function.

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: What is the average rate of change of the function f(x): = x² between x = -3 and x = 3?

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Q: Find the 3rd derivative of the function y=xsinx

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Q: Discuss how the concept of instantaneous velocity v(t) can lead to the mathematical notion of a…

A: Topic:- application of derivatives

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

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Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

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Q: Compute the derivative in terms of log for y=log(xe^(-3x))

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Q: Find the derivative of the function using 3-step rule: v (t) = -.

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Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: Find the derivative of y =log2x

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Q: Find the equilibria of the differential eq

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Q: The growth of a sunflower during the first 100 days after sprouting is modeled well by the logistic…

A: Growth rate at point of infection-

Q: compute the derivative. f (x) = ln(ex − 4x)

A: We can use chain rule ( Nested function form ) of differentiation to find the derivative. According…

Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: find derivative       1. y = ln 3x + x    2. y = ln (t2)    3. y = ln (3/ x)    4. y = ln (u + 1) -…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: how do you find the second derivative of f(x)=ln(x)?

A: on differentiation we get

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Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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Q: Calculate the second derivative y : Vx - /y = 1

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Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: Find the first derivative y= etanx

A: We have to find first derivative of    y=etanx   First derivative is dydx

Q: Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of…

A: First we will find value of y from given equation And differentiate wrt to t

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

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Q: dx V9-x2

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the…

A: Derivative rule for bx. The derivative of fx=bx is given by f'x=bx lnb.

Q: How can you relate antiderivatives as an opposite of derivatives in your life?

A: Solution:   Antiderivatives are the inverse operations of derivatives or the backward operation…

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A: Rate of change.

Q: How to solve for the second derivative?

A: The objective is to solve for the second derivative. Consider a function fx=3x4

Q: What is the difference of antidifferentiation and anti-derivative?

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Q: Solve for the derivative of the function using chain rule. 7. f(x)= sin(e3x)

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Q: Find the instantaneous rate of change of y =- at x = a

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Q: solve the first and second derivative of Y= (1+lnx)  /  x

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Q: Find the differential of the function y=lntan2x at x=π/8.

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Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

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Q: Determine the instantaneous rate of change of the function f(x) x4 at the point where x = -2.

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Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

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Q: Find the 3rd derivative of the function y=exx.

A: Differentiating with respect to x, we get Again differentiating with respect to x, we get

Q: what is the second derivative of -y/x

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Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

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A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.