Let t represent the total number of hours that a truck driver spends during a year driving on a certain highway connecting two cities, and let p(t) represent the probability that the driver will have at least one accident during these t hours. Then, 0 ≤ p(t) ≤ 1, and 1 - p(t) represents the probability of not having an accident. Under ordinary conditions, the rate of increase in the probability of an accident (as a function of t) is proportional to the probability of not having an accident. Construct and solve a differential equation for this situation.

Q: Let g(x) = f(t) dt, where ƒ is the function whose graph is given below. 0.4 0.2 - 3 -0.2- (a) At…

A: Given, gx=∫0xft dt Graph of the function f is shown as: Concept used: A critical point c is the…

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A:

Q: 25. For the function f(x) = 45x3 - 3x5, determine the interval(s) for which f(x) decreases. O (3, 3)…

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Q: ) determine the rate of increase of the infection by sovid19 outhreak size A with respect to p the…

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A:

Q: Let f(x) = 9 – x². a) Compute each of the following expressions and interpret each as an average…

A: As per our norms we have to write three multiple questions at a time kindly repost remaining…

Q: Find the linearization L(x) of the function at f(x) = x4 + 2x2, a = 1 L(x) =

A:

Q: 8. Consider the function f(x)=/25-x² . a. Find the linearization L(x) of f(x) at x=3.

A: Given expression is , fx=25-x2 to find out the linearization L(x) of f(x) at x=3.

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A:

Q: 4. Find the range of the function F(x)=√36-t² dt O [0, 36π] O [0, 18π] O [-6, 6] O [-6, 0]

A:

Q: If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

A: If (x1, f(x1)) and (x2, f(x2)) are distinct points on the graph of a function f, the average rate of…

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A: Given query is to find the value of A(2) and A'(2).

Q: Calculate the average rate of change of the given function f over the intervals [a, a + h] where h =…

A: The Average rate of change of f over the interval a, a+h is Average rate of change of f =…

Q: Let f(x) =x² t2X. Find all the values of ċ in the interval [2,0] such that f (c) =0.

A:

Q: Let A(x) f(t)dt, with f(x) shown in the graph below. -3- ** * T?

A: As per the fundamental theorem of calculus, given a function A(x)=∫0xf(t) dt, the derivative of this…

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Q: Let A > 0 be a fixed but unspecified constant, and let f(x) = xn= (In x)", x > 1. Compute f'(x).

A: our objective is to find the derivative

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A: The given function fx=sinx, a=π6

Q: If f(t) is a real valued function defined for positive values of t then L[f(t)] is given by a. e*…

A: Using definition of Laplace transform for any real valued function ft, L{ft}=∫0∞e-stf(t)dt   , t≥0

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A:

Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

A:

Q: Let A(x) | f(t)dt where f is the function given by the graph below. 2 -1 -1 -2 -3 A(1) = | A'(1) =

A:

Q: Calculate the average rate of change of the given function f over the intervals [a, a + h] where h =…

A:

Q: Let A(r) =| f(t)dt where f is the function given by the graph below. 4+ -2 -3 А(2) - А (2) - in en

A: Given:

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A: (a) From the graph f(8) = 3 and f(1) = 2

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A:

Q: Let f(x)=x3−3x2−x+4f(x)=x3−3x2−x+4. Find the average rate of change in the function over the…

A:

Q: The table below shows the average rates of change for points near In (2) for the function f(x) = e +…

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A: Follow the steps.

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A: Given: ⇒f(x)=-2x3

Q: The function f(x, y) -{¹. - x² - y², 0, if if x² + y² 1 , is continuous

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Q: Find the linearization L(x)of the function at a .

A:

Q: A continuous real-valued function f (x) with f (a) ƒ (b) < 0 , has at least one root in [a, b]

A: This question is related to Real Analysis.

Q: Let A(x) = | f(t) dt for function f shown below. Evaluate A"(5). 2 1 2 4 6. 3.

A: Use the concept of derivative of integration and slope of a curve.

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A:

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A:

Q: Let f(x) = x2. Find the net change in the value of f between the given inputs. (a) From 1 to 3…

A: Given: fx=x2 To Find: The net change in the value of f between the given inputs:  (a) From 1 to 3…

Q: 3 12. Determine the average rate of change of the function f (x) = · over the interval[-1, ÷| ? x²…

A:

Q: Let A(x) = | f(t)dt where f is the function given by the graph below. 4. -2 -3 A(5) = on to N

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Q: Let f(x)=√x+4. Find a point c that satisfies the Mean Value Theorem for the function on the interval…

A: Now differentiating f(x) with respect to x, we get Now,

Q: 47. Sketch the graph of an increasing function f such that both f'(x) and A(x) = | f (t) dt are…

A:

Q: Let A(x) = f(t)dt, with f(x) shown in the graph below.

A: Given that: Graph of f(x)

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A: Given: The interval given is [0,6]. Total change of f(t) over the interval [0,6] is determined as…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.