Consider the function f(x) = s x (1 – x) with x E [0, 1] . Is f contractive on its domain? Make sure to give a detailed proof of your assertion. Hint: It might be helpful to graph the function.

Q: If f(x) = ∫0 x   (1 - t^2)e^t^2 dt , on what interval is f increasing?

A: To determine the interval on which f is increasing. f(x)=∫0x(1-t2)et2dt

Q: the function f is not differentiable at x=0.

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

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Q: What is the Laplacian of the following function? f(x,y,z)= x² - y² +z?

A: Given function is f(x,y,z)=x^2 -y^2 +z^2. We have to find Laplacian of the function f(x,y,z) .

Q: Find the absolution extrema of f(x) = (In x)2 on [1, e].

A: We have to determine absolute extrema of girls question

Q: Find linearization L(x) of f(x) = tanh=' at a= 0 and use it to estimate f(0.01).

A: Topic:- linearisation

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: 1. Given the function 2r + 1, r 1 Verify whether or not the function f is continuous at r 1.

A: the given function is: fx=2x+1,     x≤14x2-1,       x>1 we have to verify whether or not the…

Q: Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c € R. %3D

A: Let us assume that: g(x)=sin(x)and h(x)=(x2+3x+1)So,…

Q: Let F(x) be the function defined as follows: F(x)= (1+ In(t))*dt What is the value of F'(e) ?

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Q: Differentiate the function with respect to the independer X f(x) = +e5x + e 2 e (x) = 0

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Q: "For a continuous function f(x), defined on an interval a , b, we have d f(x) dx = f(x), dx a…

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

A:

Q: Determine the domain of the function and prove that it is continuous on its domain f(x) = e - x 2

A: Consider the given function. fx=e-x2 The function is define for every real value of x. Hence,…

Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

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

A:

Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

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Q: Let = (x – 3)(x – 1)2 for a differentiable function f which is defined on the interval [0,4]. %3D dx

A: TO FIND THE CRITICAL POINTS, INTERVALS OF INCREASE AND DECREASE VALUE OF 'X' AT WHICH LOCAL EXTREMA…

Q: (b) Test the continuity of the function f(x) =|[x] + sgn(x)| at x = 0. I t function differentiable…

A: For the given function:                                        f(x)=|x+sgn(x)| We need to check if…

Q: Let f(z) (x-iy)e- ) Determine the points at which exist, and find r(2) at these points.

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

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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 F as a function of x and evaluate it at x = 0, x = 1/3, and x = T/2. F(x) = cos e de 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)…

Q: What value of c makes the following function continuous at (0, 0)? f(x) = с, x + y² + 5, (x, y) #…

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Q: Determine whether the function f (z)= Įz² – e3z I0

A:

Q: 25. Use the definition of differentiability to prove that the following function is differentiable…

A: First let us find the partial derivatives of the given function f(x,y)=x+y as shown below:…

Q: Show  that the function Z =1/2(eysinx - e-ySin(x) satisfies the La Place’s equation  =0

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

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

A:

Q: Let u be a differentiable function of x, in exercise 123, the following result is proved. P -[[] =…

A: hx=7xcos3x We need to find the derivative of the given function

Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx>1

Q: Consider the function: f(x)= (5/x^3)-(4/x^7), x>0   Let F(x) be the antiderivative of f(x) with…

A: Consider the function It can be written as

Q: Let g be a continuous function. Using the substitution u = 3x – 1, the integral (g (3x – 1)) dx is…

A: We can use the concept of method of substitution in order to solve the given problem.

Q: 6. Let f be a continuous function such that f (x) dx = 9 and f(x) dx = 13. J5 What is the value of |…

A:

Q: Find the linear approximation L(x)of f(x)=x^4 at the point a = −5 L(x)=

A: Given that f(x) = x4 We have to find the linear approximation L(x) of f(x)=x4 at the point a= -5.

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

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

A:

Q: 3. If f(x) = (1–- t²)e*dt, on what interval is the curve y =f(x) upward? concave

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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>0.…

Q: Find the values of a and b such that f is differentiable at x = 3

A: Given,            The function is fx=ax+bx≤32x1-1x>3To find : Find the values of a and b such…

Q: Verify the condition of Rolle's theorem for the function y = f(x) = e xe[-1] ] f'(c) = 0 and find C…

A: Rolle's theorem: If f(x) is a real-valued function defined on a,b such that; 1). f(x) is continuous…

Q: 10.3.13. f(x, y) = xy ln(x² + y²).

A:

Q: Find the value of fa) which makes f(x) continuous at x = a (if exists) where X - x f(x) a =

A: Given function is fx=x-xx Find the value of fa=0.

Q: Suppose that f(x) is a continuous function on the interval [0, T] . If f(x)=(sin x)ª for 0<x<T, then…

A: we have to find the value of given function. the solution is following.

Q: Let f : (0,∞) → (0,∞) be given by f(x) = ln(2 + x). Prove that f has a fixed point located between 1…

A: The given problem is to prove that the function f(x) has a fixed point in between 1 and 1.2 Given…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.