1. Find the average value of the function f(x) = x³ + 3x + 5 on [0,2].

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

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Find the equation of the normal line (NL) to the graph f(x)=x³ – 4x atx = 3 .

A: We need to find derivative.

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

A:

Q: Find the maximum rate of change of the following function at the given point. f(x, y, z) = x² + 5xz…

A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

Q: 23. Find the most general antiderivative of the functions: a) f(x) = 1 –- x³ + 5x5 – 3x7. 5 – 4.x3 +…

A: Given: 1.fx=1-x3+5x5-3x7 2.g(x)=5-4x3+3x6x6 we want to calculate the antiderivative is nothing but…

Q: Find the minimum and maximum of A over a particular interval [0,6]. A(x) = f(t) dt

A: The solution is given below in the next step: I

Q: Find the linearization of the function f (x) = x' at x = 1. a ab Va |a| sin (a) 7 х-6 L (x) Using…

A: Given a function,

Q: Find the linearization of the function given below at the specified point. f(x) 4 In(x) at a = 1…

A:

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

A: The function f(x)=2 cos 2x on the interval 0,π

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

A:

Q: Find the linear approximation L (x) to ƒ (x) = xcosx at a = T.

A: Given that, f(x) = x cosx and we have to find linear approximation L(x) at a = π

Q: 1. Show the marginal PDF of X. 2. Find P(X >Y). 3. Find P( < X s }).

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the average of the given function on the given interval. (a) y = cos x, [0, 3π/2] (b) y = x² +…

A: a) y=cos x, 0, 3π2b) y=x2+x+1, 0,1

Q: Find the linearization of the function f (x) = x° at æ = 1. L(2) = Using this linearlization, f…

A:

Q: If A(x)= f(t)dt is increasing on [0,10], then f(x) must be increasing on [0,10].

A: Given,A(x)=∫0x f(t) dt

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 linearization of the function given below at the specified point. f(x) 2 In(x) at a = 1…

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Q: Find the linearization of the function given below at the specified p f(x) = 4 In(x) at a = 1 L(x) =…

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Q: The linear approximation at x = and where B is: 0 to 1 X is A + Bx where A is:

A:

Q: Consider the For at function y= In(x+1) . what valves" of x is y undefined ?

A: The given function is y=ln (x+1) We know that, for the function ln x, x&gt;0

Q: suppose that y is an implicit function f(x) defined by the equation x^3 + y^3 = 8xy − 7. find the…

A: suppose that y is an implicit function f(x) defined by the equationx3+y3=8xy−7. find the equation of…

Q: Find the linearization L(x)of f(x)at x = a where f(x) = Vx² + 9 at a = –4

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Q: 1. Find the linearization for f(x) = In(x) at x= e. (b) Use your linearization to approximate…

A:

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)…

A:

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 marginal value such that function f given f(x) =x2+ax+1 is strictly increasing on (1,2)

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

A: Follow next step

Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: 2. Find and classify all the extrema of the function f (x, y) = 4xye e-(x²+y²)/4

A: The given function is:  f(x,y) = 4xy e-(x^2 +y^2)/4

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

A:

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

A: To find the linearization of the following function

Q: Find the linearization of the function f (x) = x6 at x = 1. L (x) = Using this linearlization, f…

A:

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: -2 In(x) Consider the function f(x, y) 3y

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Q: find ∇f at the given point. ƒ(x, y, z) = x2 + y2 - 2z2 + z ln x, (1, 1, 1)

A: Given function is fx,y,z=x2+y2-2z2+zlnx and point=1,1,1

Q: Verify Young's Theorem f(x,y) = e(2x+y) In(xy)

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Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

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Q: Suppose f(x, y)= g(x)h(y), where g and h are continuously differentiable functions of one variable…

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Q: Find the average velocity of the function over the given interval. 3 y=2 (4.7] y = x-2 3 OA. O A. 10…

A: Note: As per our guidelines, we are supposed to answer only one question. Kindly repost the other…

Q: Find the linearization L(x) of the function at a. п f(x) = sin(x), a = 6 L(x) =

A:

Q: 2. Consider the three functions below: S(z) = 2z S(z) =r S(x) = 2"

A: fx=2x,fx=x2 and fx=2x (a) Take the value of x as -2,-1,0,1,2,3. x fx=2x fx=x2 fx=2x -2 -4 4 14…

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: Test the following function for relative extrema. S(x, y)-+y -2x +2y-2xy

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Q: Consider the following function: f(r) = 2r + 3z² – 12z Find the critical numbers of f. (x = ?)

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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 points (x, f(x)) of the graph of f(x) = x4 − 4x3 − 2x 2 + 8x + 12 such that the normal line…

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