Compute the average value of the function f(x) = (7x2 + 5x + 24)ex on the interval [−5, 7].

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Q: ive of f(x, y, z) 1) in the dired

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Q: The linearization of ex at x = 1 Estimate to five decimal places the magnitude of the error involved…

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Q: S(r) = In (r² + 2x + 5)

A: SOLUTION-

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Q: Find the average rate of change of f(x) with respect to x on the interval. f(x)= x^2 -5x+1; [-3,0]

A: f(x)=x2-5x+1;-3,0 We need to find the average rate change of f(x)

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A: linearlization of f(x) at x=a is  L(x) = f(a) + (x-a)f'a)

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Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

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A: We will find the average rate of change of the function.  We know,  the average rate of change =…

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Q: A:- Find the orthogonal trajectories for functions In -1) = - COS X +a y

A: The given family of curves is: lny-1y=-cos x+a ,            where a is an arbitrary constant.

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Q: Find the best linear approximation to f(x) = x² on the interval [0, 2].

A: Here we use Taylor's approximation.

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Q: Find the average rate of change of the function over the interval [-2, 1] f(x) = 2.x³ – 5.x +3

A: To determine the average rate of change of the below function over the interval [-2,1]. fx=2x3−5x+3

Q: Find the average of the function g (x) = 2 cos 2x on the interval [0, r] -T

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A: Given that: f(x)=x2+3

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Q: Find the linear approximation to f(x) = at a = 4.

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A: while finding out the local linear approximation of any function f(x), what we do is to determine…

Q: Find the linear approximation of f(x) = (5 + x)n at x = 0. Use the approximation to estimate the…

A: fx=5+xn at x=0. Differentiating with respect to x, we get f'x=n5+xn-1 Now, f0=5+0n=5n &…

Q: Find the best linear approximation to f on th e interval [0, 1].                            f (x)…

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Q: Find the linear approximation to f(x) = (x+2) at 0 and use it to approximate (2.001)

A: Given :           f(x) = (x + 2)5 at 0 To find :             The linear approximation of f(x)…

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A: Answer is in next step.

Q: Find the average vale ot f(x)=Dx²e-2x overthe interval [-1,1]

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Q: Find the best linear approximation, g, to f on the interval [0, 1]. (x) = 2/x g(x) %3D

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Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a =. 3 L(x) =

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Q: Find the best linear approximation to f(x) = ex on the interval [-1,1]

A: We have to find the best linear approximation of f(x)=ex on the interval -1,1.

Q: Find the linearization L(x) of the function at a. f(x) = sin(x), a = 3 L(x)

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Q: 42. f(x) = sec² x, [

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Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of at x = 1. %3D df-1 - dx

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Q: Find the linear approximation of the function at the give f(x.y) = 3x y at (- 6,9) O A. L(x,y) = -…

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Q: Find the linear approximation of f(x) = Vx +I at a = 1.

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Q: Find the extreme values of the function f at the region of x2 + y² = 4 where: F (x, y) =x² + 2y²-2y…

A: The extrema of the function can be calculated by calculating the derivatives of the function. First…

Q: What is the average rate of change of f(X)= X2-2 on the interval [-1,3]?

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Q: Find the average rate of change of the function f(x) = 2x- 4x 8, on the interval r E [-3,2]. |3D

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Q: Find the local linear approximation L (x)of the function f (x) = lnx at x = 1 %3D

A: LINEAR APPROXIMATION

Q: The average revenue is defined as the function R(x) Ř(z) (x > 0) Prove that if a revenue function…

A: Let Rx denotes the revenue function. The average revenue function is defined by Rx=Rxx where x>0.…

Q: Consider the function f(x) = 4x° + 7x® – 9z³ – 10. %3D Enter the general antiderivative of f(æ)

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Q: Integrate f(x) = 10 ( 1 – x)9 where 1 ≤ x ≤ 3, Using Boole’s rule

A: The function f(x)=101-x9 where 1≤x≤3. We have to integrate this integral using the Boole's Rule.

Q: Find the maximum value of J (x) f(x) = V1 + x² on the indicated interval. [0,2]

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Q: Confirm the approximations by using the linear approximation at x = 0

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Q: Find the average rate of change of the function f(x) = x 5x - 1, over the interval [-1,3

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