Find the average value of the function f(x)= (3x +15.x-7) (2.x +5) over the given interval [1,3].

Q: Find the linearization of the function f (x) = x' at x = 1. L (x) =

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Q: S(r) = In (r² + 2x + 5)

A: SOLUTION-

Q: The derivative of f(r, y) at P(1,2) in th in the direction of-2j is -3. Then the of -i - 2j is

A: It is given that the directional derivative of f(x,y)  at P0(1,2) in the direction of (i+j) is = 22…

Q: The integrating factor of the LDE y' = x - 2ycotx is

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Q: How can we minimize the error of an approximation in a linear approximation at the point (a. f (a))?…

A: Query- How can we minimise the error of an approximation in a linear approximation at the point…

Q: Find the linearization of f(x) = (1+ x)20 at x = 0. Use it to approximate (1.001)20.

A:

Q: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

Q: Given f (x,y) = x³ + y3 – 3y² – 3x² – 9y, find the critical points and use the Second Derivative…

A: solution :-

Q: Using a local linear approximation of f(x) = v4 + x at a 0 to estimate the value of v4.3 gives

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Q: Find the linearization L(x) to the function f(x)= Vx+4 at x =4, then use the linearization to…

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

Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

A:

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

A: Here we use Taylor's approximation.

Q: Find the relative extrema using both the first and second derivative tests. f(r) = 2x³ – 9x² + 12x.…

A: Consider: fx=2x3-9x2+12x. Critical point is the point where the derivative of the function is either…

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function.  F(x) = (1 / x) , a = 2

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Q: Find the local linear approximation L (x)of the function f (x)= x² +3 at x = 1

A: Given that: f(x)=x2+3

Q: 8. What is the relationship between a and b so that F(x, y) = (ary, 3ax + bry) is source free?

A: That's easy. Have a great day!!!

Q: Determine the average rate of change of f(x)=2x+1 on the interval 4<x<5. a) f Ax b) Af Ax = 2 O d) 4…

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Q: Use a linear approximation to estimate f(0,1), given that y=f(X) is a differentiable  with f(0)=1…

A: Consider the given information

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

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Q: Determine the RMS Value of y=root x over the range of x=0 and x=1

A: We have to find the rms value of the given function over the given interval.     This problem can be…

Q: Find the derivative of f (x y z) = x^3 − xy^2 − z at (1, 1, 0) P0 in the direction of A = 2i - 3j +…

A: Given,           f(xyz)=x3−xy2−z  and point Po =(1,1,0) and the direction vector A=2i-3j+6k.

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 &amp;…

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

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Q: 3.Find the linear approximation to f(x) = cos x at x, = ÷ and use the linear approximation to…

A: We will use formula for linear approximation.

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)…

Q: Find the linearization of the function f (x) = x³ at x = 1. L(x) = Using this linearlization, ƒ…

A: Answer is in next step.

Q: Graph the function f(t)=(t − 1)² and find its average value over the interval [0,3].

A: Follow next step

Q: The average rate of change of fx) = ax' Over the interval osxs1 IS a

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

A:

Q: What is the equation of the normal line of f(x) = ln(x² – 3) at the point x = 2 ? %3D

A: Given:fx=lnx2-3  at a point x=2

Q: Find the local linear approximation L (x) of the function f(x) = 5 – x² at =2.

A: To find the linear approximation of given function.

Q: Find the linearization of the function f (x) = x° at z = 1.

A: Given, f(x)=x6

Q: Find the linear approximation L(x) to y = f(x) near x = a for the function. f(x) L(x) =

A:

Q: 2. Find whether the function F-(* - y' )i + (v² - 3x)j + (:² - xy is irrotational.

A:

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 particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: 42. f(x) = sec² x, [

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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 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: Integrate from f(x) = x4 from 0 to 1 by (Trapezoidal Rule) with h = 1, h = 0.5, h = 0.25 and…

A: Here, f(x)=x⁴ So, I=  Integrate from f(x) = x⁴ from 0 to 1. Now we can solve by Trapezoidal rule,…

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

A:

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&gt;0.…

Q: Find the linear approximation of f(x)=(1+x)3 at x=0. Using this approximation to estimate (1.01)3…

A: